Invertibility of operators on Hilbert space defined by frames

• Autorzy: Holub J. R.
• Języki publikacji: EN

Abstrakty

EN

In earlier papers [2], [3], the author introduced the notion of frame equivalence as a direct extension of the familiar concept of equivalence (or similarity) of Schauder bases in Banach spaces. In this paper we return to the topic of equivalent frames in a Hilbert space, first proving a characterization of such frames, then using this result as motivation for the solution of a problem concerning the properties of certain operators on a Hilbert space defined in a natural way by pairs of frames.

Słowa kluczowe

EN

frame; Hilbert space operator

PL

operator przestrzeni Hilberta; ramka

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2002
• Tom: Vol. 50, no 3
• Strony: 251--254
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Holub J. R.

• Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123, USA

Bibliografia

• [1] R. Duffin, A. Schaeffer, A class of non-harmonic Fourier series, Trans. Amer. Math. Soc., 72 (1952) 341-366.
• [2] J. Holub, Pre-frame operators, Besselian frames, and near-Riesz bases in Hilbert space, Proc. Amer. Math. Soc., 122 (1994) 779-785.
• [3] J. Holub, The equivalence of frames, Bull. Ac. Pol.: Math., 45 (1997) 73-76.