Factoring absolutely summing operators through Hilbert-Schmidt operators
نویسندگان
چکیده
منابع مشابه
G-frames and Hilbert-Schmidt operators
In this paper we introduce and study Besselian $g$-frames. We show that the kernel of associated synthesis operator for a Besselian $g$-frame is finite dimensional. We also introduce $alpha$-dual of a $g$-frame and we get some results when we use the Hilbert-Schmidt norm for the members of a $g$-frame in a finite dimensional Hilbert space.
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If X,Y are normed spaces, let B(X,Y ) be the set of all bounded linear maps X → Y . If T : X → Y is a linear map, I take it as known that T is bounded if and only if it is continuous if and only if E ⊆ X being bounded implies that T (E) ⊆ Y is bounded. I also take it as known that B(X,Y ) is a normed space with the operator norm, that if Y is a Banach space then B(X,Y ) is a Banach space, that ...
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Ruth Curtain Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands. E-mail:[email protected], Kalle Mikkola Helsinki University of Technology, Institute of Mathematics, Box 1100, 02015 HUT, Finland. E-mail:[email protected], Amol Sasane Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom....
متن کاملg-frames and hilbert-schmidt operators
in this paper we introduce and study besselian $g$-frames. we show that the kernel of associated synthesis operator for a besselian $g$-frame is finite dimensional. we also introduce $alpha$-dual of a $g$-frame and we get some results when we use the hilbert-schmidt norm for the members of a $g$-frame in a finite dimensional hilbert space.
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The notion of absolutely (p; q)-summing linear operators is due to A. Pietsch [18] and B. Mitiagin and A. Pe lczyński [14], inspired by previous works of A. Grothendieck. The nonlinear theory of absolutely summing operators was initiated by A. Pietsch and a complete nonlinear approach was introduced by M.C. Matos [12]. Let X,Y be Banach spaces over a fixed scalar field K = R or C; for 1 ≤ p < ∞...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1989
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500007643