A quantitative version of the Bishop-Phelps theorem for operators in Hilbert spaces

Authors
Cheng, Li Xin Dong, Yun Bai
Citation
Cheng, Li Xin et Dong, Yun Bai, A quantitative version of the Bishop-Phelps theorem for operators in Hilbert spaces, Acta mathematica Sinica. English series (Print) , 28(10), 2012, pp. 2107-2114
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
28
Issue
10
Year of publication
2012
Pages
2107 - 2114
Database
ACNP
SICI code
Abstract
In this paper, with the help of spectral integral, we show a quantitative version of the Bishop-Phelps theorem for operators in complex Hilbert spaces. Precisely, let H be a complex Hilbert space and 0 < . < 1/2. Then for every bounded linear operator T: H . H and x 0 . H with .T. = 1 = .x 0. such that .Tx 0. > 1 . g3, there exist x . . H and a bounded linear operator S: H . H with .S. = 1 = .x . . such that .Sx..=1,.x..x0..2....+2....4,.S.T..2.....