Proof of the Paszkiewicz's conjecture about a product of positive contractions

Autor:	Ando, Hiroshi, Miyamoto, Yuki, Ozawa, Narutaka
Rok vydání:	2024
Předmět:	Mathematics - Functional Analysis Mathematics - Operator Algebras Mathematics - Spectral Theory 47A63 47A65
Druh dokumentu:	Working Paper
Popis:	The Paszkiewicz conjecture about a product of positive contractions asserts that given a decreasing sequence $T_1\ge T_2\ge \dots$ of positive contractions on a separable infinite-dimensional Hilbert space, the product $S_n=T_n\dots T_1$ converges strongly. Recently, the first named author verified the conjecture for certain classes of sequences. In this paper, we prove the Paszkiewicz conjecture in full generality. Moreover, we show that in some cases, a generalized version of the Paszkiewicz conjecture also holds. Comment: version 2: The third named author (Ozawa) has found a full proof of the Paszkiewicz conjecture. Thus, most of the intermediate results from the previous version are removed. 10 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2405.10770 Zobrazit plný text záznamu View this record from Arxiv