Related papers: On holomorphic mappings with relatively $p$-compac…

We systematically derive general properties of continuous and holomorphic functions with values in closed operators, allowing in particular for operators with empty resolvent set. We provide criteria for a given operator-valued function to…

We exhibit a Banach space $Z$ failing the approximation property, for which there is an uncountable family $\mathscr F$ of closed subideals contained in the Banach algebra $\mathcal K(Z)$ of the compact operators on $Z$, such that the…

The paper is largely concerned with the possibility of obtaining a series representation for a compact linear map $T$ acting between Banach spaces. It is known that, using the notions of $j-$eigenfunctions and $j-$% eigenvalues, such a…

The behaviour of the generalized Hilbert operator associated with a positive finite Borel measure $\mu$ on $[0,1)$ is investigated when it acts on weighted Banach spaces of holomorphic functions on the unit disc defined by sup-norms and on…

In this paper, for $p\in(1,\infty)$ we study $p$-complete boundedness of weighted homomorphisms on the $p$-analog of the Fourier-Stieltjes algebras, $B_p(G)$, based on the $p$-operator space structure defined by the authors. Here, for a…

The main result is that the only non trivial closed ideal in the Banach algebra $L(L^p)$ of bounded linear operators on $L^p(0,1)$, $1\le p < \infty$, that has a left approximate identity is the ideal of compact operators. The algebra…

Let $E$, $F$ be separable Hilbert spaces, and assume that $E$ is infinite-dimensional. We show that for every continuous mapping $f:E\to F$ and every continuous function $\varepsilon: E\to (0, \infty)$ there exists a $C^{\infty}$ mapping…

Let $ E $ be a space of holomorphic functions on the unit ball $ B_X $ of a Banach space $ X.$ In this work, we introduce a Banach structure associated to $ E $ on the linear space $ WE(Y) $ containing $ Y$-valued holomorphic functions on $…

We study Hardy--Sobolev spaces H_n^p(C^+) on the upper half-plane for 1<=p<=infty and n is a nonnegative integer, from both function-theoretic and operator-theoretic viewpoints. We establish an isometric boundary characterization of…

Let ${\mathcal B}(H)$ denote the Banach algebra of all bounded linear operators on a complex Hilbert space $H$ with $\dim H\geq 3$, and let $\mathcal A$ and $\mathcal B$ be subsets of ${\mathcal B}(H)$ which contain all rank one operators.…

We construct various examples of non-trivial closed ideals of the compact-by-approximable algebra $\mathfrak{A}_X =:\mathcal K(X)/\mathcal A(X)$ on Banach spaces $X$ failing the approximation property. The examples include the following:…

We characterize the semigroups of composition operators that are strongly continuous on the mixed norm spaces $H(p,q,\alpha)$. First, we study the separable spaces $H(p,q,\alpha)$ with $q<\infty,$ that behave as the Hardy and Bergman…

Given an operator ideal I, a Banach space E has the I-approximation property if operators on E can be uniformly approximated on compact subsets of E by operators belonging to I. In this paper the I- approximation property is studied in…

Let D be a relatively compact strongly pseudoconvex domain in a Stein manifold, and let Y be a complex manifold. We prove that the set A(D,Y), consisting of all continuous maps from the closure of D to Y which are holomorphic in D, is a…

We show that a bounded linear operator on a Banach space with closed range has range-kernel complementarity if and only if its generalized amplitude is less than $\pi$. An application to the strong convergence of the iterations of a bounded…

Let $E$ be a Banach space and $A$ be a commutative Banach algebra with identity. Let ${P}(E, A)$ be the space of $A$-valued polynomials on $E$ generated by bounded linear operators (an $n$-homogenous polynomial in ${P}(E,A)$ is of the form…

We generalise the notions of scalar-valued holomorphic $p$-contact and $s$-symplectic structures introduced recently on compact complex manifolds by the second-named author jointly with H. Kasuya and L. Ugarte to their analogues with values…

Among other things, it is shown that there exist Banach spaces $Z$ and $W$ such that $Z^{**}$ and $W$ have bases, and for every $p\in[1,2)$ there is an operator $T:W\to Z$ that is not $p$-nuclear but $T^{**}$ is $p$-nuclear.

We consider 1d-Dirac operator $\mathcal L_{P,U}$ acting in $\mathbb H=(L_2[0,\pi])^2$ \begin{gather*} \ell(\mathbf y) = B\mathbf y + P(x)\mathbf y,\qquad B = \begin{pmatrix}-i&0\\0&i\end{pmatrix},\\ P(x) = \begin{pmatrix}p_1(x)&p_2(x)\\…

Let $\lambda$ be an infinite cardinal number and let $\ell_\infty^c(\lambda)$ denote the subspace of $\ell_\infty(\lambda)$ consisting of all functions that assume at most countably many non-zero values. We classify all infinite dimensional…