Naslov
On frames for countably generated Hilbert C*-modules

Autori
Arambašić, Ljiljana

Izvornik
Proceedings of the American Mathematical Society (0002-9939) 135 (2007), 2; 469-478

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Hilbert C*-module ; frame

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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