Surjectivity of linear operators from a Banach space into itself

Complex Banach Space of Bounded Linear Operators

Let X be a set, let Y be a non empty set, let F be a function from [: C, Y :] into Y , let c be a complex number, and let f be a function from X into Y . Then F ◦(c, f) is an element of Y X . We now state the proposition (1) Let X be a non empty set and Y be a complex linear space. Then there exists a function M1 from [: C, (the carrier of Y ) X :] into (the carrier of Y ) such that for every C...

Banach Space of Bounded Linear Operators

Let X be a set, let Y be a non empty set, let F be a function from [: R, Y :] into Y , let a be a real number, and let f be a function from X into Y . Then F ◦(a, f) is an element of Y X . One can prove the following propositions: (1) Let X be a non empty set and Y be a non empty loop structure. Then there exists a binary operation A1 on (the carrier of Y ) X such that for all elements f , g of...

Integral Representation of Linear Continuous Operators from the Space of Lebesgue-bochner Summable Functions into Any Banach Space.

On the Defect Indices of Linear Operators in Banach Space

The authors show that the theory of defect indices of Hermitian operators in a Hilbert space can be extended to the case of linear operators in a Banach space. For this purpose they use the idea of aperture (gap) of two subspaces with whose help it is convenient to establish in many cases the equality of the dimensions of the subspaces of the Banach space. The authors also arrive at several geo...

Weak Banach-Saks property in the space of compact operators

For suitable Banach spaces $X$ and $Y$ with Schauder decompositions and‎ ‎a suitable closed subspace $mathcal{M}$ of some compact operator space from $X$ to $Y$‎, ‎it is shown that the strong Banach-Saks-ness of all evaluation‎ ‎operators on ${mathcal M}$ is a sufficient condition for the weak‎ ‎Banach-Saks property of ${mathcal M}$, where for each $xin X$ and $y^*in‎ ‎Y^*$‎, ‎the evaluation op...