Special Additive and Multiplicative Commutator Representations for Diagonal Operators

✍ Scribed by E. Scholz; W. Timmermann

• Publisher: John Wiley and Sons
• Year: 1991
• Tongue: English
• Weight: 492 KB
• Volume: 150
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19911500106

✦ Synopsis

Abetract. Let 9) be a dense linear subspace of a separable Hilbert space and let f+(9)) be the maximal Op*-Algebra on 9). The paper deals with a class of diagonal operators of f + ( . B ) , for which we can prove some results concerning special commutator representations. For this end ideas of [ 11 are generalized.

the fact that not all orthonormal bases (y,,) 5 a are admissible in the sense that ZJ = Dw(S), 8 -(a,,), (y,,). As a first step it would be useful to investigate the following question. Suppose A = A+ € Zp(a), A -(a,,), (x,,), (xn) an orthonormal base. How far is (x,,) from being admissible?