Bounded Approximate Identities in the Algebra of Compact Operators on a Banach Space
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...
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and Applied Analysis 3 Step 1. Let F {a} be singleton. Then, there are u ∈ U and v ∈ V such that ‖uv‖ < M, and ‖ u, v, a − a‖ < M 1 . 2.2 Letting w uv ◦ uv, then ‖ uv ◦ uv, a − a‖ ‖ u, v, u, v, a − a − u, v, a − a ‖ < . 2.3 Step 2. Let F {a1, a2}. There is a u1, v1 ∈ U × V such that ‖ u1, v1, a1 − a1‖ < / 1 M , and for u1, v1, a2 − a2 ∈ A there is a u2, v2 ∈ U × V such that ‖ u2, v2, u1, v1, a2...
متن کاملThe Banach Algebra of Bounded Linear Operators
The papers [21], [8], [23], [25], [24], [5], [7], [6], [19], [4], [1], [2], [18], [10], [22], [13], [3], [20], [16], [15], [9], [12], [11], [14], and [17] provide the terminology and notation for this paper. Let X be a non empty set and let f , g be elements of X . Then g · f is an element of X . One can prove the following propositions: (1) Let X, Y , Z be real linear spaces, f be a linear ope...
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 کاملBanach Algebra of Bounded Complex Linear Operators
The terminology and notation used here are introduced in the following articles: [18], [8], [20], [5], [7], [6], [3], [1], [17], [13], [19], [14], [2], [4], [15], [10], [11], [9], and [12]. One can prove the following propositions: (1) Let X, Y , Z be complex linear spaces, f be a linear operator from X into Y , and g be a linear operator from Y into Z. Then g · f is a linear operator from X in...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1993
ISSN: 0002-9939
DOI: 10.2307/2159539