Related papers: Operator ideals on non-commutative function spaces

In this paper we give a various conditions for which the tuple $\mathcal{T} = (T_{1} , T_{2} , ... , T_{n})$ of commutative bounded linear operators on an infinite dimensional ( real , complex ) Banach space X is orbit reflexive. After we…

Let $X$ be a ball Banach function space on ${\mathbb R}^n$. Let $\Omega$ be a Lipschitz function on the unit sphere of ${\mathbb R}^n$,which is homogeneous of degree zero and has mean value zero, and let $T_\Omega$ be the convolutional…

We show for $2\le p<\infty$ and subspaces $X$ of quotients of $L_{p}$ with a $1$-unconditional finite-dimensional Schauder decomposition that $K(X,\ell_{p})$ is an $M$-ideal in $L(X,\ell_{p})$.

Let $T$ be an operator on Banach space $X$ that is similar to $- T$ via an involution $U$. Then $U$ decomposes the Banach space $X$ as $X = X_1 \oplus X_2$ with respect to which decomposition we have $U = \left(\begin{matrix} I_1 & 0 \\ 0 &…

We study best approximations to compact operators between Banach spaces and Hilbert spaces, from the point of view of Birkhoff-James orthogonality and semi-inner-products. As an application of the present study, some distance formulae are…

In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results.…

This article introduces classes of normal and unitary operators on smooth Banach spaces, providing extensions of the classical notions of normal and unitary operators from Hilbert spaces to the smooth Banach space setting. The proposed…

Let $X$ and $Y$ be separable Banach spaces and denote by $\sss\sss(X,Y)$ the subset of $\llll(X,Y)$ consisting of all strictly singular operators. We study various ordinal ranks on the set $\sss\sss(X,Y)$. Our main results are summarized as…

We investigate the duality and norm completeness in the classes of limitedly--L-weakly compact and Dunford--Pettis--L-weakly compact and operators from Banach spaces to Banach lattices.

Let $\mathcal H$ be a complex infinite-dimensional separable Hilbert space, and let $\mathcal K(\mathcal H)$ be the $C^*$-algebra of compact linear operators in $\mathcal H$. Let $(E,\|\cdot\|_E)$ be a symmetric sequence space. If…

If $p\in [1,+\infty]$ and $T$ is a linear operator with $p$-nuclear adjoint from a Banach space $ X$ to a Banach space $Y$ then if one of the spaces $X^*$ or $Y^{***}$ has the approximation property, then $T$ belongs to the ideal $N^p$ of…

A theorem of Giesy and James states that $c_0$ is finitely representable in James' quasi-reflexive Banach space $J_2$. We extend this theorem to the $p$th quasi-reflexive James space $J_p$ for each $p \in (1,\infty)$. As an application, we…

Let $T$ be a bounded linear operator on a (real or complex) Banach space $X$. If $(a_n)$ is a sequence of non-negative numbers tending to 0. Then, the set of $x \in X$ such that $\|T^nx\| \geqslant a_n \|T^n\|$ for infinitely many $n$'s has…

We study the problem of extension and lifting of operators belonging to certain operator ideals, as well as that of their associated polynomials and holomorphic functions. Our results provide a characterization of $\mathcal{L}_1$ and…

We study approximate Birkhoff-James orthogonality of bounded linear operators defined between normed linear spaces $\mathbb{X}$ and $\mathbb{Y}.$ As an application of the results obtained, we characterize smoothness of a bounded linear…

Suppose $X$ is a locally solid vector lattice. It is known that there are several non-equivalent spaces of bounded operators on $X$. In this paper, we consider some situations under which these classes of bounded operators form locally…

The theory of one-sided $M$-ideals and multipliers of operator spaces is simultaneously a generalization of classical $M$-ideals, ideals in operator algebras, and aspects of the theory of Hilbert $C^*$-modules and their maps. Here we give a…

Let $(E,\mathcal E,\mu)$ be a measure space and $G\colon E\times E\to [0,\infty]$ be measurable. Moreover, let $\mathcal F\!_{ui}$ denote the set of all $q\in\mathcal E^+$ (measurable numerical functions $q\ge 0$ on $E$) such that…

We characterize the limited operators by differentiability of convex continuous functions. Given Banach spaces $Y$ and $X$ and a linear continuous operator $T: Y \longrightarrow X$, we prove that $T$ is a limited operator if and only if,…

We give an example of an operator with different weak and strong absolutely continuous subspaces, and a counterexample to the duality problem for the spectral components. Both examples are optimal in the scale of compact operators.