Related papers: A geometric characterization of range-kernel compl…

Here Lq-Lp boundedness of integral operator with operator-valued kernels is studied and the main result is applied to convolution operators. Using these results Besov space regularity for Fourier multiplier operator is established.

We prove that the tangential Cauchy-Riemann operator has closed range on Levi-pseudoconvex CR manifolds that are embedded in a q-convex complex manifold $X$. Our result generalizes the known case when $X$ is a Stein manifold.

Let~$\mathcal{A}$ be an almost disjoint family of subsets of an infinite set~$\Gamma$, and denote by~$X_{\mathcal{A}}$ the closed subspace of~$\ell_\infty(\Gamma)$ spanned by the indicator functions of intersections of finitely many sets…

A theorem of H\"ubner states that non-round boundary points of the numerical range of a linear operator, i.e. points where the boundary has infinite curvature, are contained in the spectrum of the operator. In this note, answering a…

We prove new monotonicity properties for joint and generalized spectral radius and their essential versions of weighted geometric symmetrizations of bounded sets of positive kernel operators on $L^2$. To our knowledge, several proved…

A bounded linear operator $T$ on a Banach space $X$ is called subspace-hypercyclic if there is a subspace $M \subsetneq X$ and a vector $x \in X$ such that $orb{(x,T)} \cap M$ is dense in $M$. We show that every Banach space supports…

It is shown that the property of being bounded below (having closed range) of weighted composition operators on Hardy and Bergman spaces can be tested by their action on a set of simple test functions, including reproducing kernels. The…

We completely characterize the Crawford number attainment set and the numerical radius attainment set of a bounded linear operator on a Hilbert space. We study the intersection properties of the corresponding attainment sets of numerical…

We study certain interpolation and extension properties of the space of regular operators between two Banach lattices. Let $R_p$ be the space of all the regular (or equivalently order bounded) operators on $L_p$ equipped with the regular…

We extend the notions of joint and generalized spectral radii to cocycles acting on Banach spaces and obtain a version of Berger-Wang's formula when restricted to the space of cocycles taking values in the space of compact operators.…

Let $W$ and $Z$ be Banach spaces such that $Z$ is separable and let $R:W\longrightarrow Z$ be a (continuous, linear) operator. We study consequences of the adjoint operator $R^\ast$ having non-separable range. From our main technical result…

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…

Let $\Omega\subset\mathbb{C}$ be an open set. We show that $\overline{\partial}$ has closed range in $L^{2}(\Omega)$ if and only if the Poincar\'e-Dirichlet inequality holds. Moreover, we give necessary and sufficient potential-theoretic…

This work is devoted to the advanced study of Roper--Suffridge type extension operators. For a given non-normalized spirallike function (with respect to an interior or boundary point) on the open unit disk of the complex plane, we construct…

We study a notion analogous to the $p$-Approximation Property ($p$-AP) for Banach spaces, within the noncommutative context of operator spaces. Referred to as the $p$-Operator Approximation Property ($p$-OAP), this concept is linked to the…

Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the…

The Berezin range of a bounded operator $T$ acting on a reproducing kernel Hilbert space $\mathcal{H}$ is the set $\text{Ber}(T)$ := $\{\langle T\hat{k}_{x},\hat{k}_{x} \rangle_{\mathcal{H}} : x \in X\}$, where $\hat{k}_{x}$ is the…

We deal with kernel theorems for modulation spaces. We completely characterize the continuity of a linear operator on the modulation spaces $M^p$ for every $1\leq p\leq\infty$, by the membership of its kernel to (mixed) modulation spaces.…

We characrterize extreme contractions defined between \ finite-dimensional polyhedral Banach spaces using $k$- smoothness of operators. We also explore weak L-P property, a recently introduced concept in the study of extreme contractions.…

We identify subsets of the joint numerical range of an operator tuple in terms of its joint spectrum. This result helps us to transfer weak convergence of operator orbits into certain approximation and interpolation properties for powers in…