2013/12/02 by Stephen Bruce Sontz, Sontz, Stephen Bruce
Mathematics · Physics and Astronomy · #47B35 #81S99 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Physics (quant-ph) #math-ph #math.MP #math.OA #msc:47B35 #msc:81S99 #quant-ph
paper · pdf · doi:10.48550/arxiv.1312.0588
12 pages
arxiv created 2013/12/02 · openalex publication_date 2013/12/02 · arxiv updated 2013/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This note is a follow-up to a recent paper by the author. Most of that theory is now realized in a new setting where the vector space of symbols is not necessarily an algebra nor is it equipped with an inner product, although it does have a conjugation. As in the previous paper one does not need to put a measure on this vector space. A Toeplitz quantization is defined and shown to have most of the properties as in the previous paper, including creation and annihilation operators. As in the previous paper this theory is implemented by densely defined Toeplitz operators which act in a Hilbert space, where there is an inner product, of course. Planck's constant also plays a role in the canonical commutation relations of this theory.