Multiplicative characterization of Hilbert spaces and other interesting classes of Banach spaces
نویسندگان
چکیده
منابع مشابه
some properties of fuzzy hilbert spaces and norm of operators
in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...
15 صفحه اولBanach Spaces and Hilbert Spaces
A sequence {vj} is said to be Cauchy if for each > 0, there exists a natural number N such that ‖vj−vk‖ < for all j, k ≥ N . Every convergent sequence is Cauchy, but there are many examples of normed linear spaces V for which there exists non-convergent Cauchy sequences. One such example is the set of rational numbers Q. The sequence (1.4, 1.41, 1.414, . . . ) converges to √ 2 which is not a ra...
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Motivated by a question of Vincent Lafforgue, we study the Banach spaces X satisfying the following property: there is a function ε → ∆ X (ε) tending to zero with ε > 0 such that every operator T : L 2 → L 2 with T ≤ ε that is simultaneously contractive (i.e. of norm ≤ 1) on L 1 and on L ∞ must be of norm ≤ ∆ X (ε) on L 2 (X). We show that ∆ X (ε) ∈ O(ε α) for some α > 0 iff X is isomorphic to ...
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Let X be a NLS. Consider the set of all bounded linear functionals on X, and associate the norm defined above (as an exercise verify that it is indeed a norm). The resulting space, denoted X∗, is called the dual of X. It is another exercise to verify that X∗ is a Banach space (even if X isn’t). We can also consider the double dual X∗∗. It is easy to show that X is naturally imbedded in X∗∗ by t...
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ژورنال
عنوان ژورنال: Revista Matemática Complutense
سال: 1996
ISSN: 1988-2807,1139-1138
DOI: 10.5209/rev_rema.1996.v9.17545