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On frames for countably generated Hilbert C*-modules (CROSBI ID 116831)

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Arambašić, Ljiljana On frames for countably generated Hilbert C*-modules // Proceedings of the American Mathematical Society, 135 (2007), 2; 469-478. doi: 10.1090/S0002-9939-06-08498-X

Podaci o odgovornosti

Arambašić, Ljiljana

engleski

On frames for countably generated Hilbert C*-modules

Let V be a countably generated Hilbert C*-module over a C*-algebra A. We prove that a sequence {; ; f(i) : i is an element of I}; ; subset of V is a standard frame for V if and only if the sum Sigma(i is an element of I) < x, f(i)> < f(i), x > converges in norm for every x is an element of V and if there are constants C, D > 0 such that C parallel to x parallel to(2) = parallel to Sigma(i is an element of I)< x, f(i)> < f(i), x > parallel to <= D parallel to x parallel to(2) for every x is an element of V. We also prove that surjective adjointable operators preserve standard frames. A class of frames for countably generated Hilbert C*-modules over the C*-algebra of all compact operators on some Hilbert space is discussed.

Hilbert C*-module ; frame

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Podaci o izdanju

135 (2)

2007.

469-478

objavljeno

0002-9939

1088-6826

10.1090/S0002-9939-06-08498-X

Povezanost rada

Matematika

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