m at h . FA ] 1 F eb 2 00 5 Refinements of Reverse Triangle Inequalities in Inner Product Spaces ∗
نویسندگان
چکیده
Refining some results of S. S. Dragomir, several new reverses of the triangle inequality in inner product spaces are obtained.
منابع مشابه
ar X iv : m at h / 03 08 27 0 v 1 [ m at h . FA ] 2 8 A ug 2 00 3 SOME BOAS - BELLMAN TYPE INEQUALITIES IN 2 - INNER PRODUCT SPACES
Some inequalities in 2-inner product spaces generalizing Bessel's result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral inequalities are also provided.
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Refining some results of S. S. Dragomir, several new reverses of the generalized triangle inequality in inner product spaces are given. Among several results, we establish some reverses for the Schwarz inequality. In particular, it is proved that if a is a unit vector in a real or complex inner product space (H; 〈., .〉), r, s > 0, p ∈ (0, s],D = {x ∈ H, ‖rx− sa‖ ≤ p}, x1, x2 ∈ D − {0} and αr,s ...
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We consider BMO spaces of operator-valued functions, among them the space of operator-valued functions B which define a bounded paraproduct on L(H). We obtain several equivalent formulations of ‖πB‖ in terms of the norm of the ”sweep” function of B or of averages of the norms of martingales transforms of B in related spaces. Furthermore, we investigate a connection between John-Nirenberg type i...
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was first discovered by M. Petrovich in 1917, [5] (see [4, p. 492]) and subsequently was rediscovered by other authors, including J. Karamata [2, p. 300 – 301], H.S. Wilf [6], and in an equivalent form by M. Marden [3]. The first to consider the problem of obtaining reverses for the triangle inequality in the more general case of Hilbert and Banach spaces were J.B. Diaz and F.T. Metcalf [1] who...
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In 1964, Gähler 1 introduced the concept of 2-norm and 2-inner product spaces as generalization of norm and inner product spaces. A systematic presentation of the results related to the theory of 2-inner product spaces can be found in the book in 2, 3 and in list of references in it. Generalization of 2-inner product space for n ≥ 2 was developed by Misiak 4 in 1989. Gunawan and Mashadi 5 in 20...
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