Vol. 4, No. 3, 2011

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${\rm P}_1$ subalgebras of $M_n(\mathbb C)$

Stephen Rowe, Junsheng Fang and David R. Larson

Vol. 4 (2011), No. 3, 213–250
Abstract

A linear subspace B of L(H) has the property P1 if every element of its predual B has the form x + B with rank(x) 1. We prove that if dimH 4 and B is a unital operator subalgebra of L(H) which has the property P1, then dimB dimH. We consider whether this is true for arbitrary H.

Keywords
property $\mathrm P_1$, 2-reflexive
Mathematical Subject Classification 2000
Primary: 47L05, 47L75
Secondary: 47A15
Milestones
Received: 28 February 2010
Revised: 14 June 2011
Accepted: 16 June 2011
Published: 13 March 2012

Communicated by Charles R. Johnson
Authors
Stephen Rowe
Department of Mathematics
Texas A&M University
College Station, Texas 77843-3368
United States
Junsheng Fang
School of Mathematical Sciences
Dalian University of Technology
Dalian 116024
China
David R. Larson
Department of Mathematics
Texas A&M University
College Station, Texas 77843-3368
United States
http://www.math.tamu.edu/~larson