Related papers: A Lifting Theorem for Locally Convex Subspaces of …

A continuous linear operator $T:E \to F$ is called strictly singular if it cannot be invertible on any infinite dimensional closed subspace of its domain. In this note we discuss sufficient conditions and consequences of the phenomenon…

We first generalize the results of Le\'on and M\"uller [Studia Math. 175(1) 2006] on hypercyclic subspaces to sequences of operators on Fr\'echet spaces with a continuous norm. Then we study the particular case of iterates of an operator T…

We prove a criterion for continuity of bilinear maps on countable direct sums of topological vector spaces. As a first application, we get a new proof for the fact (due to Hirai et al. 2001) that the map taking a pair of test functions on…

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…

In this note we prove that if a sublinear operator T satisfies a certain weighted estimate in the $L^{p}(w)$ space for all $w\in A_{p}$, $1<p<+\infty$, then the operator norm of T on $L^{p}(w)$ is a continuous function of the weight $w$,…

It is proved that every operator from a weak$^*$-closed subspace of $\ell_1$ into a space $C(K)$ of continuous functions on a compact Hausdorff space $K$ can be extended to an operator from $\ell_1$ to $C(K)$.

We treat some questions related to supercyclicity of continuous linear operators when acting in locally convex spaces. We extend results of Ansari and Bourdon and consider doubly power bounded operators in this general setting. Some…

For a locally convex vector space (l.c.v.s.) $E$ and an absolutely convex neighborhood $V$ of zero, a bounded subset $A$ of $E$ is said to be $V$-dentable (respectively, $V$-f-dentable) if for any $\epsilon>0$ there exists an $x\in A$ so…

In this paper we show that every bounded linear operator T on a Hilbert space H has a closed non-trivial invariant subspace.

Let $\mathcal{H}$ be an infinite dimensional real or complex separable Hilbert space. We introduce a special type of a bounded linear operator $T$ and its important relation with invariant subspace problem on $\mathcal{H}$: operator $T$ is…

Given a map $B\to B\mathrm{Top}(n)$ of spaces, one can define a version $\mathbb{E}_{B}$ of the little cubes operad, whose construction is due to Lurie. We show that $\mathbb{E}_{B}$ enjoys the universal property that, for every…

We prove a version of the Stokes formula for differential forms on locally convex spaces. The main tool used for proving this formula is the surface layer theorem proved in another paper by the author. Moreover, for differential forms of a…

There are several proofs of the classical commutant lifting and intertwining lifting theorems in the literature. In this article, we present analogous proofs to a few $Q$-commuting lifting and $Q$-intertwining lifting theorems. We provide…

In this paper, we consider the locally convex spaces of entire functions with growth given by proximate orders, and study the representation as a differential operator of a continuous homomorphism from such a space to another one. As a…

We study the relation of $L$-equivalence, which derives from the construction of the free locally convex spaces, through a concept that particularizes several notions related to the simultaneous extension of continuous functions. We also…

We prove that for certain classes of pseudoconvex domains of finite type, the Bergman-Toeplitz operator $T_{\psi}$ with symbol $\psi=K^{-\alpha}$ maps from $L^{p}$ to $L^{q}$ continuously with $1< p\le q<\infty$ if and only if…

Let $S$ be a finite set with $n$ elements in a real linear space. Let $\cJ_S$ be a set of $n$ intervals in $\nR$. We introduce a convex operator $\co(S,\cJ_S)$ which generalizes the familiar concepts of the convex hull $\conv S$ and the…

Our main technical tool is a principally new property of compact narrow operators which works for a domain space without an absolutely continuous norm. It is proved that for every K\"{o}the $F$-space $X$ and for every locally convex…

We prove an abstract criterion that a surjective convolution operator in spaces of analytic functions on convex subsets of the complex plane has a continuous linear right inverse. Considered convex sets have a countable neighborhood basis…

The Riesz-Kantorovich formula expresses (under certain assumptions) the supremum of two operators $S, T : X \to Y$ where $X$ and $Y$ are ordered linear spaces as $$ S \vee T (x) = \sup_{0 \leqslant y \leqslant x} [S (y) + T (x - y)]. $$ We…