A polynomially bounded operator on Hilbert space which is not similar to a contraction

Journal of the American Mathematical Society

Volumn 10, Issue 2, 1997, Pages 351-369

  Pisier, Gilles ^a,b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347168951     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0894-0347-97-00227-0     Document Type: Article

References (40)

1. A. B. Aleksandrov and V. V. Peller. Hankel operators and similarity to a contraction, Internat. Math. Res. Notices 1996, no. 6, 263-275. CMP 96:11
2. O. Bratteli and D. Robinson, Operator algebras and quantum statistical mechanics II. Springer Verlag, New York, 1981. MR 82k:82013
3. ∞ . Acta Math. 152 (1984). 1-48. MR 85j:46091
4. J. Bourgain, On the similarity problem for polynomially bounded operators on Hilbert space, Israel J. Math. 54 (1986), 227-241. MR 88h:47024
5. D. Blecher and V. Paulsen, Tensor products of operator spaces, J. Funct. Anal. 99 (1991), 262-292. MR 93d:46095
6. D. Burkholder, Distribution function inequalities for martingales, Ann. Probab. 1 (1973). 19-42. MR 51:1944
7. p spaces. Academic Press. New York, 1970. MR 42:3552
8. R. Durrett, Brownian motion and martingales in analysis, Wadsworth Math. Series, Belmont (California) (1984). MR 87a:60054
9. E. Effros and Z. J. Ruan, A new approach to operator spaces, Canadian Math. Bull. 34 (1991), 329-337. MR 93a:47045
10. S. Foguel, A counterexample to a problem of Sz. Nagy, Proc. Amer. Math. Soc. 15 (1964). 788-790. MR 29:2646
11. p-spaces of several variables, Acta Math. 129 (1972), 137-193. MR 56:6263
12. C. Foias and J. P. Williams, On a class of polynomially bounded operators, Preprint (unpublished, 1979 or 1980?).
13. A. Garsia, Martingale inequalities: seminar notes on recent progress, Benjamin, Reading, MA, 1973. MR 56:6844
14. U. Haagerup, Injectivity and decomposition of completely bounded maps, in Operator Algebras and their Connection with Topology and Ergodic Theory. Springer Lecture Notes in Math. 1132 (1985), 170-222. MR 87i:46133
15. P. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887-933. MR 42:5066
16. P. Halmos. On Foguel's answer to Nagy's question, Proc. Amer. Math. Soc. 15 (1964), 791-793. MR 29:2647
17. M. Junge and G. Pisier, Bilinear forms on exact operator spaces and B(H) ⊗ B(H). Geometric and Functional Analysis (GAFA Journal) 5 (1995), 329-363. MR 96i:46071
18. A. Lebow, A power bounded operator which is not polynomially bounded. Mich. Math. J. 15 (1968), 397-399. MR 38:5047
19. F. Lust-Piquard and G. Pisier, Noncommutative Khintchine and Paley inequalities, Ark. Mat. 29 (1991), 241-260. MR 94b:46011
20. J. von Neumann, Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes. Math. Nachr. 4 (1951), 49-131. MR 13:254a
21. N. Nikolskii, Treatise on the shift operator, Springer Verlag, Berlin, 1986. MR 87i:47042
22. V. Paulsen, Completely bounded maps and dilations, Pitman Research Notes in Math., vol. 146, Longman, Wiley, New York, 1986. MR 88h:46111
23. V. Paulsen, Every completely polynomially bounded operator is similar to a contraction. J. Funct. Anal. 55 (1984), 1-17. MR 86c:47021
24. V. Paulsen, The maximal operator space of a normed space, Proc. Edinburgh Math. Soc. (2) 39 (1996). no. 2, 309-323. CMP 96:14
25. L. Page, Bounded and compact vectorial Hankel operators, Trans. Amer. Math. Soc. 150 (1970), 529-540. MR 42:8327
26. V. Peller, Estimates of functions of power bounded operators on Hilbert space, J. Oper. Theory 7 (1982), 341-372. MR 83i:47019
27. V. Peller, Estimates of functions of Hilbert space operators, similarity to a contraction and related function algebras, Research Problems, Springer Lecture Notes 1043 (199) (1984). 199-204. MR 85k:46001
28. V. Peller, Vectorial Hankel operators, commutators and related operators of the Schatten eon Neumann classes, Integral Equations and Operator Theory 5 (1982), 244-272. MR 83f:47024
29. K. Petersen, Brownian motion. Hardy spaces and bounded mean oscillation. LMS Lecture Notes Series 28 (1979). MR 58:31383
30. G. Pisier, Factorization of linear operators and the Geometry of Banach spaces, CBMS (Regional Conferences of the A.M.S.) 60 (1986). Reprinted with corrections 1987. MR 88a:47020
31. G. Pisier. Factorization of operator valued analytic functions, Advances in Math. 93 (1992). 61-125. MR 93g:46075
32. G. Pisier, Multipliers and lacunary sets in non-amenable groups, Amer. J. Math. 117 (1995). 337-376. MR 96e:46078
33. G. Pisier. Similarity problems and completely bounded maps. Springer Lecture Notes 1618 (1995).
34. R. Rochberg. A Hankel type operator arising in deformation theory, Proc. Symp. Pure Math. 35 (1979). 457-458. MR 80f:12001a
35. ∞. Trans. Amer. Math. Soc. 127 (1967), 179-203. MR 34:8193
36. B. Sz.-Nagy. Completely continuous operators with uniformly bounded iterates. Publ. Math. Inst. Hungarian Acad. Sci. 4 (1959), 89-92. MR 21:7436
37. B. Sz.-Nagy and C. Foias, Harmonic analysis of operators on Hilbert space, Akademiai Kiadó, Budapest, 1970. MR 43:947
38. J. Stafney, A class of operators and similarity to contractions. Michigan Math. J. 41 (1994). 509-521. MR 95m:47061
39. N. Tomczak-Jaegermann, Banach-Mazur distances and finite dimensional operator ideals, Longman, Pitman Monographs and Surveys in Pure and Applied Math. 38 (1989). MR 90k:46039
40. S. Treil. Geometric methods in spectral theory of vector valued functions: some recent results. Operator Theory: Adv. Appl., vol. 42, Birkhauser. 1989, pp. 209-280. MR 91j:47036