Some results about operators on L1. Issue 5 (11th August 2016)

• Record Type: Journal Article
• Authors: Riel, Zachariah C.
• Is Part Of: Quaestiones mathematicae. Volume 39:Issue 5(2016)
• Page Start: 611
• Page End: 618
• Publication Date: 2016-08-11
• Subjects: 46G10 -- 47B10 -- 47B38; Operators on Lp-spaces -- vector measures -- compact operators -- completely continuous operators -- nuclear operators -- representable operators -- absolutely summing operators -- Hilbert-Schmidt operators; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2016.1177296
• Languages: English
• ISSNs: 1607-3606

Abstract

Abstract: Let (Ω, Σ, µ ) be a probability space. We give a few results about operators on L 1 ( µ ). Among these, we show that if T is a bounded linear operator on L 1 ( µ ) which acts as a Hilbert-Schmidt operator on L 2 ( µ ), then T : L 1 ( µ ) → L 1 ( µ ) is representable.