Open AccessConstructing a Lipschitz retraction from ℬ(ℋ) onto 𝒦(ℋ)
Author(s) -
Ryotaro Tanaka
Publication year - 2019
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/14536
Subject(s) - algorithm , artificial intelligence , computer science , mathematics
It is shown that each norm closed proper two-sided ideal of a von Neumann algebra is a Lipschitz retract of the algebra. In particular, there exists a Lipschitz retraction from the algebra B ( H ) \mathcal {B}(\mathcal {H}) of all bounded linear operators on a complex Hilbert space H \mathcal {H} onto the ideal K ( H ) \mathcal {K}(\mathcal {H}) consisting of all compact operators.