Related papers: Genericity and Universality for Operator Ideals

We prove that no separable Banach algebra is universal for homomorphic embeddings of all separable Banach algebras, whether embeddings are merely bounded or required to be contractive. The same holds in the commutative category. The proof…

This paper deals with study of Birkhoff-James orthogonality of a linear operator to a subspace of operators defined between arbitrary Banach spaces. In case the domain space is reflexive and the subspace is finite dimensional we obtain a…

We introduce and study the Bourgain index of an operator between two Banach spaces. In particular, we study the Bourgain $\ell_p$ and $c_0$ indices of an operator. Several estimates for finite and infinite direct sums are established. We…

We construct a general framework that generates classes of multilinear operators between Banach spaces which encompasses, as particular cases, the several classes of summing type multilinear operators that have been studied individually in…

We consider abstract Banach spaces of analytic functions on general bounded domains that satisfy only a minimum number of axioms. We describe all invertible (equivalently, surjective) weighted composition operators acting on such spaces.…

The operator algebra is introduced based on the framework of logarithmic representation of infinitesimal generators. In conclusion a set of generally-unbounded infinitesimal generators is characterized as a module over the Banach algebra.

Let $A(k)u(k)=f(k) (1)$ be an operator equation, $X$ and $Y$ are Banach spaces, $k\in\Delta\subset\C$ is a parameter, $A(k):X\to Y$ is a map, possibly nonlinear. Sufficient conditions are given for continuity of $u(k)$ with respect to $k$.…

The use of a tensor product perspective has enriched functional analysis and other important areas of mathematics and physics. The context of operator spaces is clearly no exception. The aim of this manuscript is to kick off the development…

We prove that every lattice homomorphism acting on a Banach space $\mathcal{X}$ with the lattice structure given by an unconditional basis has a non-trivial closed invariant subspace. In fact, it has a non-trivial closed invariant ideal,…

Let $A$ be a bounded linear operator on a complex Banach space $X.$ For a given $\alpha \geq 0,$ we consider the class $\mathcal{D}_{A}^{\alpha }\left( \mathbb{R} \right) $ of all bounded linear operators $T$ on $X$ for which there exists a…

We show that a positive operator between $L^p$-spaces is given by integration against a kernel function if and only if the image of each positive function has a lower semi-continuous representative with respect to a suitable topology. This…

We compute the complexity of the classes of operators $\mathfrak{G}_{\xi, \zeta}\cap \mathcal{L}$ and $\mathfrak{M}_{\xi, \zeta}\cap \mathcal{L}$ in the coding of operators between separable Banach spaces. We also prove the non-existence of…

We exhibit a general class of unbounded operators in Banach spaces which can be shown to have the single-valued extension property, and for which the local spectrum at suitable points can be determined. We show that a local spectral radius…

In this paper we first introduce the extended limit set $J_{\{T^n\}}(x)$ for a sequence of bounded linear operators $\{T_n\}_{n=1}^{\infty}$ on a separable Banach space $X$ . Then we study the dynamics of sequence of linear operators by…

What is an adequate extension of an operator ideal I to the polynomial and multilinear settings? This question motivated the appearance of the concepts of coherent sequences of polynomial ideals and compatibility of a polynomial ideal with…

Complementable operators extend classical matrix decompositions, such as the Schur complement, to the setting of infinite-dimensional Hilbert spaces, thereby broadening their applicability in various mathematical and physical contexts. This…

We generalize the classical notion of adjoint of a linear operator and the Aron-Schottenloher notion of adjoint of a homogeneous polynomial. The general notion is shown to enjoy several properties enjoyed by the classical ones, nevertheless…

For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…

Given a complex Banach space $X$ and a joint spectrum for complex solvable finite dimensional Lie algebras of operators defined on $X$, we extend this joint spectrum to quasi-solvable Lie algebras of operators, and we prove the main…

We study a specific family of symmetric norms on the algebra $\mathcal B(\mathcal H)$ of operators on a separable infinite-dimensional Hilbert space. With respect to each symmetric norm in this family the identity operator fails to attain…