Characterizations of Minimal Elements in a Non-commutative Lp-Space

Ying Zhang, Lining Jiang*

*此作品的通讯作者

科研成果: 期刊稿件文章同行评审

1 引用 (Scopus)

摘要

For 1≤p<∞, let Lp(M,τ) be the non-commutative Lp-space associated with a von Neumann algebra M, where M admits a normal semifinite faithful trace τ. Using the trace τ, Banach duality formula and Gâteaux derivative, this paper characterizes an element a∈Lp(M,τ) such that (Formula presented.) where Bp is a closed linear subspace of Lp(M,τ) and ‖·‖p is the norm on Lp(M,τ). Such an a is called Bp-minimal. In particular, minimal elements related to the finite-diagonal-block type closed linear subspaces (Formula presented.) (converging with respect to ‖·‖p) are considered, where {ei}i=1 is a sequence of mutually orthogonal and τ-finite projections in a σ-finite von Neumann algebra M, and S is the set of elements in M with τ-finite supports.

源语言英语
文章编号120
期刊Bulletin of the Malaysian Mathematical Sciences Society
47
4
DOI
出版状态已出版 - 7月 2024

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