Related papers: Quasi-Nilpotent Operators on Locally Convex Spaces

Quasianalytic contractions form the crucial class in the quest for proper invariant and hyperinvariant subspaces for asymptotically non-vanishing Hilbert space contractions. The property of quasianalycity relies on the concepts of unitary…

For Banach spaces $X$ and $Y$, a bounded linear operator $T\colon X \longrightarrow Y^*$ is said to weak-star quasi attain its norm if the $\sigma(Y^*,Y)$-closure of the image by $T$ of the unit ball of $X$ intersects the sphere of radius…

We introduce a weakened notion of norm attainment for bounded linear operators between Banach spaces which we call \emph{quasi norm attaining operators}. An operator $T\colon X \longrightarrow Y$ between the Banach spaces $X$ and $Y$ is…

For each ordinal $0\leqslant \xi\leqslant \omega_1$, we introduce the notion of a $\xi$-completely continuous operator and prove that for each ordinal $0< \xi< \omega_1$, the class $\mathfrak{V}_\xi$ of $\xi$-completely continuous operators…

In the setting of operators on Hilbert spaces, we prove that every quasinilpotent operator has a non-trivial closed invariant subspace if and only if every pair of idempotents with a quasinilpotent commutator has a non-trivial common closed…

In this paper, we define for the first time the local Morrey-type space associated with ball quasi-Banach function spaces and show the related series of properties. In addition, Hardy-Littlewood maximal operator's boundedness is proved. We…

Let $X$ be a metric space with bounded geometry, $p\in\{0\} \cup [1,\infty]$, and let $E$ be a Banach space. The main result of this paper is that either if $X$ has Yu's Property A and $p\in(1,\infty)$, or without any condition on $X$ when…

In this paper, we present some necessary and sufficient conditions for semi-compact operators being almost L-weakly compact (resp. almost M-weakly compact) and the converse. Mainly, we prove that if $X$ is a nonzero Banach space, then every…

In this paper we study sufficient conditions for an operator to have an almost-invariant half-space. As a consequence, we show that if $X$ is an infinite-dimensional complex Banach space then every operator $T\in\mathcal{L}(X)$ admits an…

We consider the action of finitely truncated singular integral operators on functions taking values in a Banach space. Such operators are bounded for any Banach space, but we show a quantitative improvement over the trivial bound in any…

If X is a sequentially complete locally convex space, then a quotient bounded operator T is regular (in the sense of Waelbroeck) if and only if it is a bounded element (in the sense of Allan) of the algebra of quotient bounded operators on…

Bounded linear operators on separable Banach spaces algebraically similar to the classical Volterra operator $V$ acting on $C[0,1]$ are characterized. From this characterization it follows that $V$ does not determine the topology of…

This paper establishes that multilinear Calder\'on--Zygmund operators and their maximal operators are bounded on Hardy spaces associated with ball quasi-Banach function spaces. Moreover, we also obtain the boundedness of multilinear…

Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in $\bf R$.…

We use the injective envelope to study quasimultipliers of operator spaces. We prove that all representable operator algebra products that an operator space can be endowed with are induced by quasimultipliers. We obtain generalizations of…

Variational inequalities, formulated on unknown dependent convex sets, are called quasi-variational inequalities (QVI). This paper is concerned with the abstract approach to a class of parabolic QVIs arising in many biochemical/mechanical…

In this survey, we discuss the definition of a (quasi-)Banach function space. We advertise the original definition by Zaanen and Luxemburg, which does not have various issues introduced by other, subsequent definitions. Moreover, we prove…

We study (almost) limited operators in Banach lattices and their relations to L-weakly compact, semi-compact, and Dunford-Pettis operators. Several further related topics are investigated.

We introduce a new class of quasi-Banach spaces as an extension of the classical Grand Lebesgue Spaces for small values of the parameter, and we investigate some its properties, in particular, completeness, fundamental function, operators…

In this paper we explore some basic properties of quasi-Banach function spaces which are important in applications. Namely, we show that they posses a generalised version of Riesz--Fischer property, that embeddings between them are always…