Journal article
The spectral picture of (LA, RB)
Journal of Functional Analysis, Vol.71(2), pp.371-392
1987
DOI: 10.1016/0022-1236(87)90010-3
Abstract
Let A and B be commuting n -tuples of operators on a Hilbert space H , and let ( L A , R B ) be the (2 n )-tuple of left and right multiplications induced by A and B on L(H) . We show that σ T ((L A ,R B ), L(H)) = σ T (A,H) × σ T (B,H) , σ Te ((L A ,R B ), L(H)) = [σ Te (A,H) × σ T (B,H)]∪[σ T (A,H) × σ Te (B,H)] , and ind( L A , R B ) = (−1) n ind( A )ind( B ), whenever A and B are Fredholm. Similar results hold for the restrictions of ( L A , R B ) to norm ideals in L(H) , giving in particular the spectral picture of ( A ⊗ I , I ⊗ B ) on H ⊗ H . A. S. Fainstein, working independently, has announced versions of these results for Banach spaces.
Details
- Title: Subtitle
- The spectral picture of (LA, RB)
- Creators
- Raúl E CurtoLawrence A Fialkow
- Resource Type
- Journal article
- Publication Details
- Journal of Functional Analysis, Vol.71(2), pp.371-392
- DOI
- 10.1016/0022-1236(87)90010-3
- ISSN
- 1096-0783
- eISSN
- 1096-0783
- Language
- English
- Date published
- 1987
- Academic Unit
- Mathematics
- Record Identifier
- 9983985807202771
Metrics
22 Record Views