Work

Proof of the Paszkiewicz conjecture about a product of positive contractions

Year: 2024

Type: article

Abstract: The Paszkiewicz conjecture about a product of positive contractions asserts that given a decreasing sequence $$T_1\ge T_2\ge \dots $$ T 1 ≥ T 2 ≥ ⋯ of positive contractions on a separable infinite-dimensional Hilbert space, the product $$S_n=T_n\dots T_1$$ S n = T n ⋯ 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.

Source: Positivity

DOI: 10.1007/s11117-024-01102-y

Authors: Hiroshi Ando, Yuki Miyamoto, Narutaka Ozawa

Institutions: Chiba University, Kyoto University, Research Institute for Mathematical Sciences, Kyoto University

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: Japan Society for the Promotion of Science