The Hahn-Banach Theorem on Arbitrary Groups
نویسندگان
چکیده
منابع مشابه
Hahn-banach Theorem
We prove a version of Hahn-Banach Theorem. and 1] provide the notation and terminology for this paper. The following propositions are true: (1) For all sets x, y and for every function f such that h hx; yi i 2 f holds y 2 rng f: (2) For every set X and for all functions f, g such that X dom f and f g holds fX = gX: (3) For every non empty set A and for every set b such that A 6 = fbg there exis...
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(2)1 For every set X and for all functions f , g such that X ⊆ dom f and f ⊆ g holds f X = g X . (3) For every non empty set A and for every set b such that A 6= {b} there exists an element a of A such that a 6= b. (4) For all sets X , Y holds every non empty subset of X→̇Y is a non empty functional set. (5) Let B be a non empty functional set and f be a function. Suppose f = ⋃ B. Then dom f = ⋃...
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was established by Hahn [1; p. 217] in 1927, and independently by Banach [2; p. 212] in 1929, who also generalized Theorem 0 for real spaces, to the situation in which the functional q :E^>R is an arbitrary subadditive, positive homogeneous functional [2; p. 226]. Theorem 0 was not established for complex spaces until 1938, when it was deduced from the real theorem by Bohnenblust and Sobczyk [3...
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ژورنال
عنوان ژورنال: Kyungpook mathematical journal
سال: 2009
ISSN: 1225-6951
DOI: 10.5666/kmj.2009.49.2.245