منابع مشابه
Banach Algebra of Bounded Functionals
Let V be a non empty additive loop structure and let V1 be a subset of V . We say that V1 has inverse if and only if: (Def. 1) For every element v of V such that v ∈ V1 holds −v ∈ V1. Let V be a non empty additive loop structure and let V1 be a subset of V . We say that V1 is additively-closed if and only if: (Def. 2) V1 is add closed and has inverse. Let V be a non empty additive loop structur...
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The notation and terminology used in this paper are introduced in the following articles: [2], [16], [9], [14], [7], [8], [3], [18], [17], [4], [19], [5], [15], [1], [20], [12], [11], [10], [21], [13], and [6]. Let V be a complex algebra. A complex algebra is called a complex subalgebra of V if it satisfies the conditions (Def. 1). (Def. 1)(i) The carrier of it ⊆ the carrier of V , (ii) the add...
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In this article, we give a definition of a functional space which is constructed from all continuous functions defined on a compact topological space. We prove that this functional space is a Banach algebra. Next, we give a definition of a function space which is constructed from all real-valued continuous functions with bounded support. We prove that this function space is a real normed space.
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...
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...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2008
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-008-0017-z