Year: 2024
Type: article
Abstract: It is known that the multiplier algebra of an approximately unital and nondegenerate L p -operator algebra is again an L p -operator algebra.In this paper we investigate examples that drop both hypotheses.In particular, we show that the multiplier algebra of T p 2 , the algebra of strictly upper triangular 2 × 2 matrices acting on ℓ p 2 , is still an L p -operator algebra for any p.To contrast this result, we first provide a thorough study of the augmentation ideal of ℓ 1 (G) for a discrete group G.We use this ideal to define a family of nonapproximately unital degenerate L p -operator algebras, F p 0 ,)ޚ3/ޚ( whose multiplier algebras cannot be represented on any L q -space for any q ∈ [1, ∞) as long as p ∈ [1, p 0 ] ∪ [ p ′ 0 , ∞), where p 0 = 1.606 and p ′ 0 is its Hölder conjugate.
Source: Pacific Journal of Mathematics
Authors: Andrey Blinov, Alonso Delfín, Ellen Weld
Institutions: University of Colorado Boulder, Sam Houston State University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4405867685