On the Helson-Szegő theorem and a related class of modified Toeplitz kernels

Cotlar, Mischa; Sadosky, Cora

doi:10.1090/pspum/035.1/545279

Cited by 81 publications

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“…In §5 we will give the distance between a given Hankel form and the set of all compact sesquilinear forms. In §6 as a result of the previous sections we will obtain a new lifting theorem which contains one due to Cotlar and Sadosky [4]. In §7 we will apply results in the previous sections to problems in weighted norm inequalities as in [3] Theorem 2 implies that \\H φ \\ = inf{|||^ + ^olll ^0 = 0}.…”

Section: Takahiko Nakazimentioning

confidence: 99%

Bounded Hankel forms with weighted norms and lifting theorems

Nakazi¹

1991

Pacific J. Math.

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Bounded Hankel forms with respect to weighted norms are studied. The Nehari's theorem about the norms of the classical Hankel forms is generalized. This is essentially a lifting theorem due to Cotlar and Sadosky. Moreover a theorem about the essential norms of Hankel forms is proved. This relates with a theorem of Adamjan, Arov and Krein in the special case and gives a new lifting theorem which has applications to weighted norm inequalities, and the F. and M. Riesz theorem.

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Section: Takahiko Nakazimentioning

confidence: 99%

Bounded Hankel forms with weighted norms and lifting theorems

Nakazi¹

1991

Pacific J. Math.

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“…This problem is related with a lifting theorem of Cotlar and Sadosky [4] for the disk algebra and a generalized lifting theorem of the author and Yamamoto [10] for a general uniform algebra. In the special case, they consider the problem above when 38 is commutative.…”

Section: A Lifting Theorem and Analytic Operator Algebras Takahiko Namentioning

confidence: 99%

“…In (2) if U is a bilateral shift with multiplicity 1, then the lifting theorem is classical and was shown by Cotlar and Sadosky (cf. [4]). We can show this using (3) and [3, Proposition 5.1].…”

Section: P€5rmentioning

confidence: 99%

A Lifting Theorem and Analytic Operator Algebras

Nakazi¹

1988

Proceedings of the American Mathematical Society

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Abstract.Let K be a complex Hubert space and H a closed subspace. It is shown that if a 2 x 2 selfadjoint operator matrix J7~ with positive diagonals on K ffi K is positive on H ffi H1-, then there exists a 2 x 2 operator matrix !? with the same diagonals such that ¿T is positive on K ffi K and ¡7 is the restriction of J7" to H ffi H-1. When !T is in a von Neumann algebra, we consider the problems of finding H~ in the same algebra. This lifting theorem has applications to weighted norm inequalities for conjugation operators on analytic operator algebras.

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“…Recently, Arocena, Cotlar and Sadosky (see [1,2,4]) have shown that this is true when A is a disc algebra. But it does not seem to be true for general uniform algebras, even for uniform algebras on finitely connected regions.…”

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confidence: 94%

A lifting theorem and uniform algebras

Nakazi¹,

Yamamoto²

1988

Trans. Amer. Math. Soc.

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Abstract. In this paper we discuss the possible generalizations of a lifting theorem of a 2 X 2 matrix to uniform algebras. These have applications to Hankel operators, weighted norm inequalities for conjugation operators and Toeplitz operators on uniform algebras. For example, the Helson-Szegö theorems for general uniform algebras follow.1. Introduction. We will consider a fixed uniform algebra A on a compact Hausdorff space X, and a fixed homomorphism t in MA, the maximal ideal space of A. The set of representing measures for t will be denoted by #T. The kernel of t will be denoted by A0. That is, A0 consists of the functions f in A such that t(/) = 0. We study only 2x2 measure matrices u. = (u, ) whose elements are finite complex regular Borel measures, and satisfy the conditions:

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On the Helson-Szegő theorem and a related class of modified Toeplitz kernels

Cited by 81 publications

References 0 publications

Bounded Hankel forms with weighted norms and lifting theorems

Bounded Hankel forms with weighted norms and lifting theorems

A Lifting Theorem and Analytic Operator Algebras

A lifting theorem and uniform algebras

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