Let $X$ and $Y$ be infinite-dimensional Banach spaces. Let $T:X\to Y$ be a linear continuous operator with dense range and $T(X)\not =Y$. It is proved that, for each $\epsilon>0$, there exists a quotient map $q: Y\to Y_1$, such that $Y_1$ is an infinite-dimensional Banach space with a Schauder basis and $q\circ T$ is a nuclear operator of norm $\leq \epsilon$. Thereby, we obtain with respect to quotient spaces the proper analogue result of KATO concernig the existence of not trivial nuclear restrictions of not open linear continuous operators between Banach spaces. As a consequence, it is derived a result of OSTROVSKII concerning Banach spaces which are completions with repsect to total nonnorming subspaces
Let l be a Banach sequence space with a monotone norm in which the canonical system (e(n)) is an unc...
We show that a Banach space X has an infinite dimensional reflexive subspace (quotient) if and only ...
In this chapter we consider the completeness problem for a more general class of bounded linear oper...
Let X and Y be infinite-dimensional Banach spaces. Let $T: X → Y$ be a linear continuous operator wi...
. This note is devoted to the answers to the following questions asked by V. I. Bogachev, B. Kirchhe...
It is proved that every infinite-dimensional non-archimedean Banach space of countable type admits ...
It is proved that every infinite-dimensional non-archimedean Banach space of countable type admits ...
AbstractIn this work we establish some basic properties of closed linear operators between nonarchim...
Given a bounded linear operator T from a separable infinite-dimensional Banach space E into a Banach...
We extend and provide a vector-valued version of some results of C. Samuel about the geometric relat...
We extend and provide a vector-valued version of some results of C. Samuel about the geometric relat...
We extend and provide a vector-valued version of some results of C. Samuel about the geometric relat...
Many of the best-known questions about separable infinite-dimensional Banach spaces are of at least ...
SummaryLet K be a complete infinite rank valued field. In [4] we studied Norm Hilbert Spaces (NHS) o...
International audience$X\sim Y$ denotes that $X$ and $Y$ are linearly isomorphic Banach spaces. Let ...
Let l be a Banach sequence space with a monotone norm in which the canonical system (e(n)) is an unc...
We show that a Banach space X has an infinite dimensional reflexive subspace (quotient) if and only ...
In this chapter we consider the completeness problem for a more general class of bounded linear oper...
Let X and Y be infinite-dimensional Banach spaces. Let $T: X → Y$ be a linear continuous operator wi...
. This note is devoted to the answers to the following questions asked by V. I. Bogachev, B. Kirchhe...
It is proved that every infinite-dimensional non-archimedean Banach space of countable type admits ...
It is proved that every infinite-dimensional non-archimedean Banach space of countable type admits ...
AbstractIn this work we establish some basic properties of closed linear operators between nonarchim...
Given a bounded linear operator T from a separable infinite-dimensional Banach space E into a Banach...
We extend and provide a vector-valued version of some results of C. Samuel about the geometric relat...
We extend and provide a vector-valued version of some results of C. Samuel about the geometric relat...
We extend and provide a vector-valued version of some results of C. Samuel about the geometric relat...
Many of the best-known questions about separable infinite-dimensional Banach spaces are of at least ...
SummaryLet K be a complete infinite rank valued field. In [4] we studied Norm Hilbert Spaces (NHS) o...
International audience$X\sim Y$ denotes that $X$ and $Y$ are linearly isomorphic Banach spaces. Let ...
Let l be a Banach sequence space with a monotone norm in which the canonical system (e(n)) is an unc...
We show that a Banach space X has an infinite dimensional reflexive subspace (quotient) if and only ...
In this chapter we consider the completeness problem for a more general class of bounded linear oper...