Tensor product of left polaroid operators
A Banach space operator T E B(X) is left polaroid if for each A E isooa{T) there is an integer d(A) such that asc(T — A) = d(A) < oo and (T-X)dW+1X is closed; T is finitely left polaroid if asc(T-A) < oo, (T — X)X is closed and dim(T — A)-1(0) < oo at each A E isoaa(T). The left polaroid pr...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2012
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| Sorozat: | Acta scientiarum mathematicarum
78 No. 1-2 |
| Kulcsszavak: | Matematika, Operátorelmélet, Banach-tér |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16431 |
| Tartalmi kivonat: | A Banach space operator T E B(X) is left polaroid if for each A E isooa{T) there is an integer d(A) such that asc(T — A) = d(A) < oo and (T-X)dW+1X is closed; T is finitely left polaroid if asc(T-A) < oo, (T — X)X is closed and dim(T — A)-1(0) < oo at each A E isoaa(T). The left polaroid property transfers from A and B to their tensor product A® B, hence also from A and B* to the left-right multiplication operator TAB> f°r Hilbert space operators; an additional condition is required for Banach space operators. The finitely left polaroid property transfers from A and B to their tensor product A® B if and only if 0 £ iso <ja{A®B)\ a similar result holds for TAB f°r finitely left polaroid A and B*. |
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| Terjedelem/Fizikai jellemzők: | 251-264 |
| ISSN: | 0001-6969 |