Browsing by Author "Harish Chandra"

Now showing 1 - 20 of 28

A CHARACTERIZATION OF ZERO DIVISORS AND TOPOLOGICAL DIVISORS OF ZERO IN C[a, b] AND ℓ∞
(Korean Mathematical Society, 2023) Harish Chandra; Anurag Kumar Patel
We give a characterization of zero divisors of the ring C[a, b]. Using theWeierstrass approximation theorem, we completely characterize topological divisors of zero of the Banach algebra C[a, b]. We also characterize the zero divisors and topological divisors of zero in ℓ∞. Further, we show that zero is the only zero divisor in the disk algebra A (D) and that the class of singular elements in A (D) properly contains the class of topological divisors of zero. Lastly, we construct a class of topological divisors of zero of A (D) which are not zero divisors © 2023 Korean Mathematical Society
Antinormal composition operators on l2(λ)
(Drustvo Matematicara Srbije, 2016) Dilip Kumar; Harish Chandra
In this paper we characterize self-adjoint and normal composition operators on Poisson weighted sequence spaces l2(λ). However, the main purpose of this paper is to determine explicit conditions on inducing map under which a composition operator admits a best normal approximation. We extend results of Tripathi and Lal [Antinormal composition operators on l2, Tamkang J. Math. 39 (2008), 347-352] to characterize antinormal composition operators on l2(λ). © 2016, Drustvo Matematicara Srbije. All rights reserved.
ANTINORMAL OPERATORS AND ANTINORMALITY OF COMPOSITION OPERATORS ON L2(X)
(Korean Mathematical Society, 2024) Arvind Bhatt; Harish Chandra; Mohammad Irshad Khan
In this article, we show that if T ∈ B(H) is an antinormal perator, M is a reducing subspace for T and i(T|M) and i(T) are of the same sign, then T|M is also antinormal. We also characterize the antinormality of composition operators on L2(X) for a σ-finite meas urespace X. © 2024 Korean Mathematical Society
Antinormal Weighted Composition Operators
(Hindawi Publishing Corporation, 2016) Dilip Kumar; Harish Chandra
Let l 2 = L 2 N, μ, where N is set of all positive integers and μ is the counting measure whose σ -algebra is the power set of N. In this paper, we obtain necessary and sufficient conditions for a weighted composition operator to be antinormal on the Hilbert space l 2. We also determine a class of antinormal weighted composition operators on Hardy space H 2 D. © 2016 Dilip Kumar and Harish Chandra.
Antinormal weighted composition operators on L2(μ) - space of an atomic measure space
(Springer, 2020) Dilip Kumar; Harish Chandra
Let L2(μ) denote the separable Hilbert space associated with a σ-finite atomic measure μ. In this paper, we determine necessary and sufficient conditions for boundedness of weighted composition transformation on L2(μ) and give a characterization of antinormal weighted composition operators on L2(μ). © 2018, The Author(s).
Antinormality and m-isometry of shift on weighted trees
(Springer Science and Business Media Deutschland GmbH, 2022) Mohammad Irshad Khan; Harish Chandra
The shift operator and its various generalizations are amongst the most widely studied operators on a Hilbert space. In this paper, we characterize antinormal and m-isometric shift operator S on the Hilbert space L2(T, λ) associated with a locally finite directed weighted tree T. We also discuss interesting connections between antinormality and m-isometry of S. © 2022, The Author(s).
Ascent and descent of composition operators on lp spaces
(Walter de Gruyter GmbH, 2010) Harish Chandra; Pradeep Kumar
Let lp (1 ≤ p ≤ ∞) be the Banach space of all p-summable sequences (bounded sequences for p - ∞) of complex numbers under the standard p-norm on it and Cφ be a composition operator on V induced by a function φ on ℕ into itself. In this paper we give a characterization of composition operators whose ascent and descent are infinite. © 2010 Warsaw University. All rights reserved.
Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions
(2010) Arvind Bhatt; Harish Chandra; D.R. Sahu
In this paper, we obtain some common fixed point theorems for occasionally weakly compatible mappings on a set X together with the function d:X×X→[0,∞) without using the triangle inequality and assuming symmetry only on the set of points of coincidence. © 2010 Elsevier Ltd. All rights reserved.
Common fixed points for JH-operators and occasionally weakly g-biased pairs under relaxed condition on probabilistic metric space
(2013) Arvind Bhatt; Harish Chandra
We obtain some fixed point theorems for JH-operators and occasionally weakly g-biased maps on a set X together with the function F: X × X → Δ without using the triangle inequality and without using the symmetric condition. Our results extend the results of Bhatt et al. (2010). © 2013 Arvind Bhatt and Harish Chandra.
Common fixed points of weakly compatible maps in symmetric spaces
(2012) Harish Chandra; Arvind Bhatt; Sanjay Pant
In this paper we obtain common fixed point theorems of weakly compatible maps on symmetric spaces. We prove that if S and T are weakly compatible maps satisfying property (E-A) along with strict contractive conditions, then they have common fixed points. Since these results are obtained without using full force of metric, they are improved generalization of results obtained by Pant ([10], [11]).
Compactness and norm of the sum of weighted composition operators on A(ⅅ)
(Hikari Ltd., 2010) Harish Chandra; Bina Singh
Let A(D{double-struck}) denote the disk algebra and uCφ be the weighted composition operator on A(D{double-struck}). In this paper, we characterize the compactness of sum of weighted composition operators on A(D{double-struck}). Furthermore, we also find the norm of sum of weighted composition operators on A(D{double-struck}).
Essential ascent and essential descent of linear operators and composition operators
(RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES, 2020) Harish Chandra; Pradeep Kumar
In this paper we prove certain results relating to essential ascent and essential descent of linear operator on an arbitrary vector space. Further, we give a complete characterization of essential ascent and essential descent of composition operators on lp spaces. © 2020, RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES. All rights reserved.
Essential ascent and essential descent of weighted composition operators on lp spaces
(RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES, 2020) Harish Chandra; Pradeep Kumar
In this paper we give a complete characterization of essential ascent and essential descent of weighted composition operators on lp spaces. © 2020, RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES. All rights reserved.
Extremal non-compactness of weighted composition operators on the disk algebra
(2010) Harish Chandra; Bina Singh
Let A(D) denote the disk algebra and Wψ,φ be weighted composition operator on A(D). In this paper we obtain a condition on ψ and φ for Wψ,φ to exhibit extremal non-compactness. As a consequence we show that the essential norm of a composition operator on A(D) is either 0 or 1.
Finite size effect on the strong absorption radius and the barrier parameters of the heavy-ion potential
(1992) Harish Chandra
The finite size effect of interacting heavy ions on the strong absorption radius of the heavy-ion potential is examined. The inclusion of the finite size contribution to the dynamic moment of inertia yields smaller values for the strong absorption radius for a given value of the grazing angular momentum. The weak energy dependence seems to be an inherent property of the strong absorption radius parameter irrespective of the size consideration of the interacting heavy ions. The finite size effect has been quantitatively demonstrated for the Ca40+40Ca heavy-ion system. The interaction potential for the system is a sum of the Coulomb interaction term and the nuclear interaction part obtained from the unified nuclear potential approach of Krappe, Nix, and Sierk. The strength of the potential is calculated for separation distances greater than the contact radius of interacting heavy ions with sharp spherical ion shapes. The Coulomb interaction term outside the contact radius corresponds to two point charge interacting ions. © 1992 The American Physical Society.
Fixed point theorems for occasionally weakly compatible maps in probabilistic semi-metric space
(2009) Harish Chandra; Arvind Bhatt
In this paper we prove common fixed point theorems for a pair of occasionally weakly compatible maps in probabilistic semi - metric space. These results are extensions of the results which we have obtained on symmetric spaces [3].
Hypercyclic and Supercyclic Composition Operator on Some Weighted Sequence Spaces
(Springer, 2025) Vijay Kumar Srivastava; Ashish Naudiyal; Harish Chandra
We consider a composition operator on some weighted ℓp(λ) spaces and describe some of its basic properties including boundedness, closed range, surjectivity, hypercyclicity, and supercyclicity. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
Hypercyclicity, supercyclicity and cyclicity of composition operators on Lp spaces
(Informatics Publishing Limited and The Indian Mathematical Society, 2019) Vijay Kumar Srivastava; Harish Chandra
In this paper, we discuss hypercyclicity, supercyclicity and cyclicity of composition operators on lp(1 ≤ p < ∞). We prove that no composition operator is hypercyclic on lp. Further, we also prove that Cφ : lp → lp is supercyclic if and only if φ is injective and φn has no fixed point in N, for any n ∈ N. We also give a sufficient condition and some necessary conditions for cyclicity of composition operator. © Indian Mathematical Society, 2019.
Hypercyclicity, supercyclicity, and cyclicity of a weighted composition operator on ℓp spaces
(De Gruyter Open Ltd, 2021) Vijay K. Srivastava; Harish Chandra
In this paper, we give a characterization of a hypercyclic weighted composition operator on ℓp (1 ≤ p < ∞). We also obtain some necessary conditions and sufficient conditions for the supercyclicity and cyclicity of a weighted composition operator on ℓp (1 ≤ p < ∞. © 2021 Walter de Gruyter GmbH, Berlin/Boston.
Importance of cell wall-associated poly-α-l-glutamine in the biology of pathogenic mycobacteria
(Springer Singapore, 2019) Rajni Garg; Rajesh Mani; Manish Gupta; Deeksha Tripathi; Harish Chandra; Rakesh Bhatnagar; Nirupama Banerjee
Mycobacterium tuberculosis (Mtb), the formidable scourge known to mankind since ancient times, has remained untamed despite vigorous scientific research in the field. In the last several decades, significant advances have been made to study this pathogen; however, a lot more remains in the realm of unknown. The complex and unique cell wall of the bacterium is a major factor contributing to the unrestrained success of the pathogen in infecting millions around the world. Since the discovery of this bacterium, numerous studies have attempted to unravel the complexities of mycobacterial cell envelop to characterize individual constituents and their importance in pathobiology of Mtb. Major components of the cell envelop of mycobacteria such as lipid-linked polysaccharides-lipoarabinomannan (LAM), dimycolyl trehalose (cord factor), sulfolipids, and mycolyl-arabinogalactan-peptidoglycan (mAGP) complex have been investigated extensively. However, a lesser known molecule, poly-α-L-glutamine/glutamate (PLG), that constitutes ~10% of dry weight of cell wall has not attracted as much attention. As early as 1990, Hirschfield et al. isolated PLG as insoluble material and showed its association with the Mtb cell wall. In the last few years, our group has been working to identify enzymes that may play a role in the synthesis/assembly and localization of this polymer in the cell wall of mycobacteria. Our recently published work has shown that PLG by itself is weakly immunogenic in mice, but when combined with protein antigens, it can stimulate different arms of the T helper-mediated responses, demonstrating its potential to act as an adjuvant (Mani et al. 2018). © Springer Nature Singapore Pte Ltd. 2019.