منابع مشابه
A Two-dimensional Hahn-banach Theorem
Let T̃ = ∑n i=1 ũi⊗ vi : V → V = [v1, ..., vn] ⊂ X, where ũi ∈ V ∗ and X is a Banach space. Let T = ∑n i=1 ui ⊗ vi : X → V be an extension of T̃ to all of X (i.e., ui ∈ X∗) such that T has minimal (operator) norm. In this paper we show in particular that, in the case n = 2 and the field is R, there exists a rank-n T̃ such that ‖T‖ = ‖T̃‖ for all X if and only if the unit ball of V is either not smo...
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The idea behind this article is to provide a unified and relatively nontechnical framework for treating the main existence theorems for continuous linear functionals in functional analysis, convex analysis, Lagrange multiplier theory, and minimax theory. While many of the results in this article are already known, our approach is new, and gives a large number of results with considerable econom...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2000
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-00-05944-x