M. A. Lihobabenko, “Block frames in the <nobr>$\ell^2$</nobr> space”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2011, Issue 2(83),Pages <nobr>38

Mathematics

Block frames in the $\ell^2$ space

M. A. Lihobabenko

Dept. of Theory of Functions and Functional Analysis, Samara State University, Samara, 443011, Russian Federation

Abstract: $\varepsilon$-nearly Parceval–Steklov infinite frames in the space $l^2_N(\mathbb{R})$ with prescribed norms are considered. This paper proposes block construction of frames in the space $\ell^2$.

Keywords: $\varepsilon$-nearly Parceval–Steklov frames, trace of operator, block-diagonal matrix, block frame.

UDC: 517.51+517.98

Received: 10.03.2011
Revised: 10.03.2011