Related papers: Minimal and Maximal Operator Space Structures on B…

Given an operator ideal I, a Banach space E has the I-approximation property if operators on E can be uniformly approximated on compact subsets of E by operators belonging to I. In this paper the I- approximation property is studied in…

We construct a family $(\mathcal{X}_\al)_{\al\le \omega_1}$ of reflexive Banach spaces with long transfinite bases but with no unconditional basic sequences. In our spaces $\mathcal{X}_\al$ every bounded operator $T$ is split into its…

Let $\mathcal{E}(X,d,\mu)$ be a Banach function space over a space of homogeneous type $(X,d,\mu)$. We show that if the Hardy-Littlewood maximal operator $M$ is bounded on the space $\mathcal{E}(X,d,\mu)$, then its boundedness on the…

We explore the relation between the orthogonality of bounded linear operators in the space of operators and that of elements in the ground space. To be precise, we study if $ T, A \in \mathbb{L}(\mathbb{X}, \mathbb{Y}) $ satisfy $ T \bot_B…

In this paper, equivalence between interpolation properties of linear operators and monotonicity conditions are studied, for a pair $(X_0,X_1)$ of rearrangement invariant quasi Banach spaces, when the extreme spaces of the interpolation are…

We study symmetric points with respect to $(\rho_+)$-orthogonality, $(\rho_{-})$-orthogonality and $\rho$-orthogonality in the space $C(K, \mathbb{X}),$ where $K$ is a perfectly normal, compact space and $ \mathbb X$ is a Banach space. We…

A Banach space $X$ has the $2$-summing property if the norm of every linear operator from $X$ to a Hilbert space is equal to the $2$-summing norm of the operator. Up to a point, the theory of spaces which have this property is independent…

It is proved that the resolvent norm of an operator with a compact resolvent on a Banach space $X$ cannot be constant on an open set if the underlying space or its dual is complex strictly convex. It is also shown that this is not the case…

We study octahedral norms in the space of bounded linear operators between Banach spaces. In fact, we prove that $L(X,Y)$ has octahedral norm whenever $X^*$ and $Y$ have octahedral norm. As a consequence the space of operators $L(\ell_1…

We study the geometry of $\mathcal{L}(X)_w,$ the space of all bounded linear operators on a Banach space $X,$ endowed with the numerical radius norm, whenever the numerical radius defines a norm. We obtain the form of the extreme points of…

Let $X$ be a reflexive Banach space. In this paper we give a necessary and sufficient condition for an operator $T\in \mathcal{K}(X)$ to have the best approximation in numerical radius from the convex subset $\mathcal{U} \subset…

We prove that if T is a strictly singular 1-1 operator defined on an infinite dimensional Banach space X, then for every infinite dimensional subspace Y of X there exists an infinite dimensional subspace Z of Y such that Z contains orbits…

This paper is about certain linear subspaces of Banach SN spaces (that is to say Banach spaces which have a symmetric nonexpansive linear map into their dual spaces). We apply our results to monotone linear subspaces of the product of a…

In this paper we study two types of collections of operators on a Banach space on the subject of forming operator ideals. One of the types allows us to construct an uncountable chain of closed ideals in each of the operator algebras…

We give examples of real Banach spaces with exactly infinite countably many complex structures and with $\omega_1$ many complex structures.

Let $E$ be a Banach function space on a probability measure space $(\Omega ,\Sigma,\mu).$ Let $X$ be a Banach space and $E(X)$ be the associated K\"{o}the-Bochner space. An operator on $E(X)$ is called a multiplication operator if it is…

Let $E,F$ be exact operators (For example subspaces of the $C^*$-algebra $K(H)$ of all the compact operators on an infinite dimensional Hilbert space $H$). We study a class of bounded linear maps $u\colon E\to F^*$ which we call tracially…

A real square matrix $A$ is called a P-matrix if all its principal minors are positive. Using the sign non-reversal property of matrices, the notion of P-matrix has been recently extended by Kannan and Sivakumar to infinite-dimensional…

A remarkable theorem of R. C. James is the following: suppose that $X$ is a Banach space and $C \subseteq X$ is a norm bounded, closed and convex set such that every linear functional $x^* \in X^*$ attains its supremum on $C$; then $C$ is a…

Let X and Y be complex Banach spaces, B_X be the open unit ball of X and HL(B_X,Y) be the Banach space of all holomorphic Lipschitz maps f:B_X->Y such that f(0)=0, endowed with the Lipschitz norm. Given a Banach operator ideal A, we use the…