相关论文: On approximately orthogonality preserving and reve…

We consider solving a probably infinite dimensional operator equation, where the operator is not modeled by physical laws but is specified indirectly via training pairs of the input-output relation of the operator. Neural operators have…

Bloch theorem for a periodic operator is being revisited here, and we notice extra orthogonality relationships. It is shown that solutions are bi-periodic, in the sense that eigenfunctions are periodic with respect to one argument, and…

We study almost L(M) weakly compact and order L(M) weakly compact operators in Banach spaces. Several further topics related to these operators are investigated.

Spaces of homogeneous polynomials on a Banach space are frequently equipped with quasinorms instead of norms. In this paper we develop a technique to replace the original quasi-norm by a norm in a dual preserving way, in the sense that the…

The $m$-point nonlocal problem for the first order differential equation with an operator coefficient in a Banach space $X$ is considered. An exponentially convergent algorithm is proposed and justified provided that the operator…

We define new symbol classes for pseudodifferntial operators and investigate their pseudodifferential calculus. The symbol classes are parametrized by commutative convolution algebras. To every solid convolution algebra over a lattice we…

We introduce a class of linear bounded invertible operators on Banach spaces, called shift operators, which comprises weighted backward shifts and models finite products of weighted backward shifts and dissipative composition operators. We…

We study recurrent operators from a new perspective by introducing the notion of hyper-recurrent operators and establish robust connections with quasi-rigid operators. For example, we prove that a recurrent operator on a separable Banach…

We study extreme contractions in the setting of finite-dimensional polyhedral Banach spaces. Motivated by the famous Krein-Milman Theorem, we prove that a \emph{rank one} norm one linear operator between such spaces can be expressed as a…

We show that any bounded operator $T$ on a separable, reflexive, infinite-dimensional Banach space $X$ admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension. In the non-reflexive spaces, we…

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…

Given commuting $d$-tuples $\mathbb{S}_i$ and $\mathbb{T}_i$, $1\leq i\leq 2$, Banach space operators such that the tensor products pair $(\mathbb{S}_1\otimes\mathbb{S}_2,\mathbb{T}_1\otimes\mathbb{T}_2)$ is strict $m$-isometric (resp.,…

The question is addressed of when a Sobolev type space, built upon a general rearrangement-invariant norm, on an $n$-dimensional domain, is a Banach algebra under pointwise multiplication of functions. A sharp balance condition among the…

We characterize bijections on matrix spaces (operator algebras) preserving full rank (invertibility) of differences of matrix (operator) pairs in both directions.

Let $A,$ $T$ and $B$ be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences $\left\{ A^{n}TB^{n}\right\} $ and…

We show that there are compact linear operators on Banach spaces which cannot be approximated by numerical radius attaining operators.

We obtain the exact values of some important approximative quantities (such as, the best approximation, the basis width, Kolmogorov's width and the best $n$-term approximation) of certain sets of images of the diagonal operators in the…

In this paper we show that a result of Gross and Kuelbs, used to study Gaussian measures on Banach spaces, makes it possible to construct an adjoint for operators on separable Banach spaces. This result is used to extend well known theorems…

It is proved that: each collectively order continuous set of operators from an Archimedean OVS with a generating cone to an OVS is collectively order bounded; and each collectively order to norm bounded set of operators from an ordered…

We consider positive, integral-preserving linear operators acting on $L^1$ space, known as stochastic operators or Markov operators. We show that, on finite-dimensional spaces, any stochastic operator can be approximated by a sequence of…