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pro vyhledávání: '"Sarkar, Jaydeb"'
We prove a Hankel-variant commutant lifting theorem. This also uncovers the complete structure of the Beurling-type reducing and invariant subspaces of Hankel operators. Kernel spaces of Hankel operators play a key role in the analysis.
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Externí odkaz:
http://arxiv.org/abs/2408.13753
Autor:
Das, Soma, Sarkar, Jaydeb
We represent closed subspaces of the Hardy space that are invariant under finite-rank perturbations of the backward shift. We apply this to classify almost invariant subspaces of the backward shift and represent a more refined version of nearly invar
Externí odkaz:
http://arxiv.org/abs/2407.17352
Given a natural number $n \geq 1$, the odometer semigroup $O_n$, also known as the adding machine or the Baumslag-Solitar monoid with two generators, is a well-known object in group theory. This paper examines the odometer semigroup in relation to re
Externí odkaz:
http://arxiv.org/abs/2405.14157
We present complete classifications of paired operators on the Hilbert space $L^2(\mathbb{T})$ and Toeplitz + Hankel operators on vector-valued Hardy spaces. We introduce the notion of inner-paired operators defined on the Hardy space that use the cl
Externí odkaz:
http://arxiv.org/abs/2404.05435
This article intends to initiate an investigation into the structure of $M$-ideals in $H^\infty(\mathbb{D})$, where $H^\infty(\mathbb{D})$ denotes the Banach algebra of all bounded analytic functions on the open unit disc $\mathbb{D}$ in $\mathbb{C}$
Externí odkaz:
http://arxiv.org/abs/2403.16947
We represent and classify pairs of commuting isometries $(V_1, V_2)$ acting on Hilbert spaces that satisfy the condition \[ [V_1^*, V_2] = \text{compact} + \text{normal}, \] where $[V_1^*, V_2] := V_1^* V_2 - V_2 V_1^*$ is the cross-commutator of $(V
Externí odkaz:
http://arxiv.org/abs/2401.10807
Orthogonal projections onto closed subspaces of $H^2(\mathbb{D}^n)$ of the form $\varphi H^2(\mathbb{D}^n)$ for inner functions $\varphi$ on $\mathbb{D}^n$ are referred to as inner projections, where $H^2(\mathbb{D}^n)$ denotes the Hardy space over t
Externí odkaz:
http://arxiv.org/abs/2307.06744
Let $\mathbb{D}$ represent the open unit disc in $\mathbb{C}$. Denote by $A(\mathbb{D})$ the disc algebra, and $\mathscr{B}(X, A(\mathbb{\mathbb{D}}))$ the Banach space of all bounded linear operators from a Banach space $X$ into $A(\mathbb{D})$. We
Externí odkaz:
http://arxiv.org/abs/2305.00859
We present complete classifications of automorphisms of two closed subalgebras of the bounded analytic functions on the open unit disc $\mathbb{D}$, namely, the subalgebra of functions vanishing at the origin, and the subalgebra of functions whose fi
Externí odkaz:
http://arxiv.org/abs/2304.01327
Autor:
D., Deepak K., Sarkar, Jaydeb
The fundamental theorem on commutant lifting due to Sarason does not carry over to the setting of the polydisc. This paper presents two classifications of commutant lifting in several variables. The first classification links the lifting problem to t
Externí odkaz:
http://arxiv.org/abs/2301.10020