RUS  ENG
Full version
JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 1997 Volume 188, Number 8, Pages 63–74 (Mi sm243)

This article is cited in 5 papers

Quasiorthogonal sets and conditions for a Banach space to be a Hilbert space

P. A. Borodin

M. V. Lomonosov Moscow State University

Abstract: For a subspace $Y$ of a Banach space $X$ the quasiorthogonal set $Q(Y,X)$ is the set of all $n\in X$ such that $0$ is one of the best approximation elements of $n$ in $Y$. The properties of the sets $Q(Y,X)$ are studied; several criteria in terms of these sets for $X$ to be a Hilbert space are established; in particular, generalizations of the well-known theorems of Rudin–Smith–Singer and Kakutani are proved.

UDC: 517.982.22

MSC: 46B20, 46C05, 41A65

Received: 25.07.1996

DOI: 10.4213/sm243


 English version:
Sbornik: Mathematics, 1997, 188:8, 1171–1182

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2025