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Aryaman Sensarma

Publications and source records attributed to Aryaman Sensarma.

7 recordsLinked to original sources
arXiv2024

A Bishop-Phelps-Bollobás theorem for bounded analytic functions

Let $H^\infty$ denote the Banach algebra of all bounded analytic functions on the open unit disc and denote by $\mathscr{B}(H^\infty)$ the Banach space of all bounded linear operators from $H^\infty$ to itself. We prove that the Bishop-Phelps-Bollobás property holds for $\mathscr{B}(H^\infty)$. As an application to our approach, we prove that the Bishop-Phelps-Bollobás property also holds for operator ideals of $\mathscr{B}(H^\infty)$.

math.FA↗
arXiv2024

Russo-Dye type Theorem, Stinespring representation,and Radon Nikodym dervative for invariant block multilinear completely positive maps

In this article, we investigate certain basic properties of invariant multilinear CP maps. For instance, we prove Russo-Dye type theorem for invariant multilinear positive maps on both commutative $C^*$-algebras and finite-dimensional $C^*$-algebras. We show that every invariant multilinear CP map is automatically symmetric and completely bounded. Possibly these results are unknown in the literature (see \cite{Heo 00,Heo,HJ 2019}). Motivated from quantum algorithm simulation \cite{BSD} we introduce multilinear version of invariant block CP map $ φ=[φ_{ij}] : M_{n}(\A)^k \to M_n(\mathcal{B({H})}).$ Then we derive that each $φ_{ij}$ can be dilated to a common commutative tuple of$*$-homomorphisms. As a natural appeal, the suitable notion of minimality has been identified within this framework. A special case of our result recovers a finer version of J. Heo's Stinespring type dilation theorem of \cite{Heo}, and A. Kaplan's Stinespring type dilation theorem \cite{AK89}. As an application, we show Russo-Dye type theorem for invariant multilinear completely positive maps. Finally, using minimal Stinespring dilation we obtain Radon Nikodym theorem in this setup.

math.OA↗
arXiv2023

A Bishop-Phelps-Bollobas theorem for disc algebra

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 prove that, under the assumption of equicontinuity at a point in $\partial \mathbb{D}$, the Bishop-Phelps-Bollobás property holds for $\mathscr{B}(X, A(\mathbb{\mathbb{D}}))$.

math.FA↗
arXiv2023

Automorphisms and generalized projections on spaces of analytic functions

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 first derivative vanishes at the origin. The later subalgebra is known as the Neil algebra. We also characterize generalized tri-circular projections on $H^{p}(\mathbb{D})$ and $H^{p}(\mathbb{D}^2)$, $1\leq p \leq \infty$, $p\neq 2$.

math.CV↗
arXiv2021

Idempotent, model, and Toeplitz operators attaining their norms

We study idempotent, model, and Toeplitz operators that attain the norm. Notably, we prove that if $\mathcal{Q}$ is a backward shift invariant subspace of the Hardy space $H^2(\mathbb{D})$, then the model operator $S_{\mathcal{Q}}$ attains its norm. Here $S_{\mathcal{Q}} = P_{\mathcal{Q}}M_z|_{\mathcal{Q}}$, the compression of the shift $M_z$ on the Hardy space $H^2(\mathbb{D})$ to $\mathcal{Q}$.

math.FA↗
arXiv2020

Orthogonality in Banach Spaces via projective tensor product

Let $X$ be a complex Banach space and $x,y\in X$. By definition, we say that $x$ is Birkhoff-James orthogonal to $y$ if $ \|x+λy\|_{X} \geq \|x\|_{X}$ for all $λ\in \mathbb{C}$. We prove that $x$ is Birkhoff-James orthogonal to $y$ if and only if there exists a semi-inner product $φ$ on $X$ such that $\|φ\| = 1$, $φ(x,x)=\|x\|^2$ and $φ(x,y)=0$. A similar result holds for $C^*$-algebras. A key point in our approach to orthogonality is the representations of bounded bilinear maps via projective tensor product spaces.

math.FA↗