Compact operators of the formuCφ
نویسندگان
چکیده
منابع مشابه
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...
متن کاملCompact Sets and Compact Operators
Proof. Properties 2 and 3 are left to the reader. For property 1, assume that S is an unbounded compact set. Since S is unbounded, we may select a sequence {vn}n=1 such that ‖vn‖ → 0 as n→∞. Since S is compact, this sequence will have a convergent subsequence, say {vk}k=1, which will still be unbounded. This sequence is Cauchy, so there is a positive integer K for which ‖v`− vm‖ ≤ 1/2 for all `...
متن کاملCompact Operators
In these notes we provide an introduction to compact linear operators on Banach and Hilbert spaces. These operators behave very much like familiar finite dimensional matrices, without necessarily having finite rank. For more thorough treatments, see [RS, Y]. Definition 1 Let X and Y be Banach spaces. A linear operator C : X → Y is said to be compact if for each bounded sequence {xi}i∈IN ⊂ X , t...
متن کاملweak 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...
متن کاملSome properties of b-weakly compact operators on Banach lattices
In this paper we give some necessary and sufficient conditions for which each Banach lattice is space and we study some properties of b-weakly compact operators from a Banach lattice into a Banach space . We show that every weakly compact operator from a Banach lattice into a Banach space is b-weakly compact and give a counterexample which shows that the inverse is not true but we prove ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1979
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1979.80.205