Related papers: Composition ideals of Lip-Linear operators and a H…

In this paper we extend the scope of three important results of the linear theory of absolutely summing operators. The first one was proved by Bu and Kranz in \cite{BK} and it asserts that a continuous linear operator between Banach spaces…

We study in this paper some property of Lipschitz mappings which admit factorization through an operator ideal. We try to construct Lipschitz cross-norms from known tensor norms in order to represent certain classes of Lipschitz mappings.…

Let $E$ and $F$ be complex Banach spaces, $U$ be an open subset of $E$ and $1\leq p\leq\infty$. We introduce and study the notion of a Cohen strongly $p$-summing holomorphic mapping from $U$ to $F$, a holomorphic version of a strongly…

The linear operators defined on the Lipschitz projective tensor product of X and E motivate the study of a distinct class of operators acting on the cartesian produc X E. This class, denoted by LipL(X E;F), combines Lipschitz and linear…

We characterize classes of linear maps between operator spaces $E$, $F$ which factorize through maps arising in a natural manner via the Pisier vector-valued non-commutative $L^p$ spaces $S_p[E^*]$ based on the Schatten classes on the…

We study hermitian operators and isometries on spaces of vector-valued Lipschitz maps with the sum norm: $\|\cdot\|_{\infty}+L(\cdot)$. There are two main theorems in this paper. Firstly, we prove that every hermitian operator on…

We study composition operators on spaces of holomorphic Lipschitz functions defined on the open unit ball of a complex Banach space. Our approach is based on the linearization of the symbol through the holomorphic Lipschitz-free spaces,…

We characterize those bounded multilinear operators that factor through a Hilbert space in terms of its behavior in finite sequences. This extends a result, essentially due to S. Kwapie\'{n}, from the linear to the multilinear setting. We…

We study the ideals of linear operators between Banach spaces determined by the transformation of vector-valued sequences involving the new sequence space introduced by Karn and Sinha \cite{karnsinha} and the classical spaces of absolutely,…

Let X and Y be complex Banach spaces, B_X be the open unit ball of X and HL(B_X,Y) be the Banach space of all holomorphic Lipschitz maps f:B_X->Y such that f(0)=0, endowed with the Lipschitz norm. Given a Banach operator ideal A, we use the…

We study those operators on a Hilbert space that can be lifted / extended to any twisted Hilbert space. We prove that these form an ideal of operators which contains all the Schatten classes. We characterize those multiplication operators…

We study a systematic way to produce a Lipschitz operator ideal from a Banach linear operator ideal $\mathcal A$. For maximal and minimal operator ideals $\mathcal A$, the Lipschitz maximal hull and minimal kernel of the Lipschitz operator…

In view of the fact that some classical methods to construct multi-ideals fail in constructing hyper-ideals, in this paper we develop two new methods to construct hyper-ideals of multilinear operators between Banach spaces. These methods…

We apply the geometric approach provided by $\Sigma$-operators to develop a theory of $p$-summability for multilinear operators. In this way, we introduce the notion of Lipschitz $p$-summing multilinear operators and show that it is…

We introduce and develop the notion of hyper-ideals of multilinear operators between Banach spaces. While the well studied notion of ideals of multilinear operators (multi-ideals) relies on the composition with linear operators, the notion…

Applying a linearization theorem due to J. Mujica, we study the ideals of bounded holomorphic mappings $\mathcal{H}^\infty\circ\mathcal{I}$ generated by composition with an operator ideal $\mathcal{I}$. The bounded-holomorphic dual ideal of…

The objective of this study is to advance the theory concerning positive summing operators. Our focus lies in examining the space of positive strongly p-summable sequences and the space of positive unconditionally p-summable sequences. We…

We construct a general framework that generates classes of multilinear operators between Banach spaces which encompasses, as particular cases, the several classes of summing type multilinear operators that have been studied individually in…

We introduce and explore the concept of positive ideals for both linear and multilinear operators between Banach lattices. This paper delineates the fundamental principles of these new classes and provides techniques for constructing…

Let $X$, $Y$ and $Z$ be Banach spaces and let $U$ be a subspace of $\mathcal{L}(X^*,Y)$, the Banach space of all operators from $X^*$ to $Y$. An operator $S: U \to Z$ is said to be $(\ell^s_p,\ell_p)$-summing (where $1\leq p <\infty$) if…