Spectral lifting in banach algebras and interpolation in several variables

Transactions of the American Mathematical Society

Volumn 353, Issue 7, 2001, Pages 2843-2857

  Popescu, Gelu ^a  

^a UNIVERSITY OF TEXAS AT SAN ANTONIO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23044527859     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-01-02796-9     Document Type: Article

References (29)

1. [AMc] J. Agler and J.E. Mc Carthy, Nevanlinna-Pick kernels and localization, preprint (1997). CMP 2000:17
2. [ArPo1] A. Arias and G. Popescu, Factorization and reflexivity on Fock spaces, Integr. Equal. Oper.Th. 23 (1995), 268-286.
3. [ArPo2] A. Arias and G. Popescu, Noncommutative interpolation and Poisson transforms, Israel J. Math. 115 (2000), 205-234.
4. [Arv] W.B. Arveson, Subalgebras of C*-algebras III: Multivariable operator theory, Acta Math. 181 (1998), 159-228. MR 2000e:47013
5. [BTV] J.A. Ball, T.T.Trent, and V. Vinnikov, Interpolation and commutant lifting for multipliers on reproducing kernel Hilbert spaces, preprint (1999).
6. [BV] J.A. Ball and V. Vinnikov, Multivariable linear systems, scattering, unitary dilations and operator theory for row contractions, preprint (1999).
7. [B] J.A. Ball, Linear systems, operator model theory and scattering: multivariable generalizations, preprint (1999).
8. [BFT] H. Bercovici, C. Foias, and A. Tannenbaum, A spectral commutant lifting theorem, Trans. Amer. Math. Soc. 325 (1991), 741-763. MR 91j:47006
9. [BF] H. Bercovici and C. Foias, On spectral tangential Nevanlinna-Pick interpolation, J.Math. Anal.Appl. 155 (1991), 156-176. MR 92d:47020
10. [DP1] K.R. Davidson and D. Pitts, Invariant subspaces and hyper-reflexivity for free semigroup algebras, Proc. London Math.Soc., 78 (1999), 401-430.
11. [DP2] K.R. Davidson and D. Pitts, The algebraic structure of non-commutative analytic Toeplitz algebras, Math. Ann. 311 (1998), 275-303. MR 20001e:47082
12. [DP3] K.R. Davidson and D. Pitts, Nevanlinna-Pick interpolation for noncommutative analytic Toeplitz algebras, Integr. Equat. Oper.Th. 31 (1998), 321-337. MR 2000g:47016
13. [DMP] R.G. Douglas, P.S. Muhly and C. Pearcy, Lifting commuting operators, Michigan Math.J. 15 (1968), 385-395. MR 38:5046
14. [F] I.P. Fedcina, A description of of the solutions of the Nevanlinna-Pick tangent problem, Akad. Nauk. Armjan. SSR Dokl. 60 (1975), 37-42. MR 52:5974
15. [N] R. Nevanlinna, Über beschränkte Functionen, die in gegebenen Punkten vorgeschribene Werte annehmen, Ann. Acad. Sci. Fenn. Ser A 13 (1919), 7-23.
16. [P] G. Pick, Über die Beschränkungen analytischer Functionen, welche durch vorgegebene Functionswerte bewirkt werden, Math. Ann. 77 (1916), 7-23.
17. [Po1] G. Popescu, Isometric dilations for infinite sequences of noncommuting operators, Trans. Amer.Math.Soc. 316 (1989), 523-536. MR 90c:47006
18. [Po2] G. Popescu, Characteristic functions for infinite sequences of noncommuting operators, J.Operator Theory 22 (1989), 51-71. MR 91m:47012
19. 1, Math.Scand. 68 (1991), 292-304. MR 92k:47073
20. [Po4] G. Popescu, On intertwining dilations for sequences of noncommuting operators, J.Math. Anal.Appl. 167 (1992), 382-402. MR 93e:47012
21. [Po5] G. Popescu, Functional calculus for noncommuting operators, Michigan Math. J. 42 (1995), 345-356. MR 96k:47025
22. [Po6] G. Popescu, Multi-analytic operators on Fock spaces, Math. Ann. 303 (1995), 31-46. MR 96k:47049
23. [Po7] G. Popescu, Noncommutative disc algebras and their representations, Proc. Amer. Math. Soc. 124 (1996), 2137-2148. MR 96k:47077
24. [Po8] G. Popescu, Interpolation problems in several variables, J.Math Anal.Appl. 227 (1998), 227-250. MR 991:47028
25. [Po9] G. Popescu, Poisson transforms on some C*-algebras generated by isometries, J. Funct. Anal. 161 (1999), 27-61. MR 2000m:46117
26. [R] G.C. Rota, On models for linear operators, Comm.Pure Appl.Math. 13 (1960), 469-472. MR 22:2898
27. ∞, Trans. AMS 127 (1967), 179-203. MR 34:8193
28. [SzF1] B.Sz.-Nagy, C. Foiaş, Dilation des commutants d'operateurs, C.R.Acad.Sci. Paris, Serie A 266 (1968), 493-495. MR 38:5049
29. [SzF2] B.Sz.-Nagy, C. Foias,̧ Harmonic analysis on operators on Hilbert space, North-Holland, Amsterdam (1970). MR 43:947