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## Studia Mathematica

1998 | 131 | 2 | 179-188
Tytuł artykułu

### Multipliers of Hardy spaces, quadratic integrals and Foiaş-Williams-Peller operators

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We obtain a sufficient condition on a B(H)-valued function φ for the operator $⨍ ↦ Γ_φ ⨍'(S)$ to be completely bounded on $H^∞ B(H)$; the Foiaş-Williams-Peller operator | S^t Γ_φ | R_φ = | | | 0 S | is then similar to a contraction. We show that if ⨍ : D → B(H) is a bounded analytic function for which $(1-r) ||⨍'(re^{iθ})||^2_{B(H)} rdrdθ$ and $(1-r) ||⨍"(re^{iθ})||_{B(H)} rdrdθ$ are Carleson measures, then ⨍ multiplies $(H^1c^1)'$ to itself. Such ⨍ form an algebra A, and when φ'∈ BMO(B(H)), the map $⨍ ↦ Γ_φ ⨍'(S)$ is bounded $A → B(H^2(H), L^2(H) ⊖ H^2(H))$. Thus we construct a functional calculus for operators of Foiaş-Williams-Peller type.
Słowa kluczowe
EN
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
179-188
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-11-26
poprawiono
1998-04-17
Twórcy
autor
• Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, England
Bibliografia
• [1] O. Blasco, On the area function for H(σ _p), 1≤ p≤ 2, Bull. Polish Acad. Sci. Math. 44 (1996), 285-292.
• [2] G. Blower, Quadratic integrals and factorization of linear operators, J. London Math. Soc. (2) 56 (1997), 333-346.
• [3] J. Bourgain, On the similarity problem for polynomially bounded operators on Hilbert space, Israel J. Math. 54 (1986), 227-241.
• [4] J. Bourgain, Vector-valued singular integrals and the $H^1$-BMO duality, in: Probability Theory and Harmonic Analysis, J. A. Chao and W. A. Woyczy/nski (eds.), Marcel Dekker, New York, 1986, 1-19.
• [5] K. R. Davidson and V. I. Paulsen, Polynomially bounded operators, J. Reine Angew. Math. 487 (1997), 153-170.
• [6] E. G. Effros and Z.-J. Ruan, On matricially normed spaces, Pacific J. Math. 132 (1988), 243-264.
• [7] C. Foiaş and J. P. Williams, On a class of polynomially bounded operators, preprint.
• [8] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981.
• [9] S. Parrott, On a quotient norm and the Sz.-Nagy-Foiaş lifting theorem, J. Funct. Anal. 30 (1978), 311-328.
• [10] V. I. Paulsen, Every completely polynomially bounded operator is similar to a contraction, ibid. 55 (1984), 1-17.
• [11] V. V. Peller, Estimates of functions of Hilbert space operators, similarity to a contraction and related function algebras, in: Linear and Complex Analysis Problem Book, V. P. Havin [V. P. Khavin], S. V. Hruščëv [S. V. Khrushchëv] and N. K. Nikol'skiĭ (eds.), Lecture Notes in Math. 1043, Springer, Berlin, 1984, 199-204.
• [12] G. Pisier, Factorization of operator valued analytic functions, Adv. Math. 93 (1992), 61-125.
• [13] G. Pisier, Similarity Problems and Completely Bounded Maps, Lecture Notes in Math. 1618, Springer, Berlin, 1995.
• [14] G. Pisier, A polynomially bounded operator on Hilbert space which is not similar to a contraction, J. Amer. Math. Soc. 10 (1997), 351-369.
Typ dokumentu
Bibliografia
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