共查询到10条相似文献,搜索用时 78 毫秒
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Summary We prove that the maximal conjugate and Hilbert operators are not bounded from the real Hardy space H1 to L1, where the underlying spaces may be over T or R. We also draw corollaries for the corresponding spaces over T2 and R2. 相似文献
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《Indagationes Mathematicae》2022,33(2):494-516
Current work defines Schmidt representation of a bilinear operator , where and are separable Hilbert spaces. Introducing the concept of singular value and ordered singular value, we prove that if is compact, and its singular values are ordered, then has a Schmidt representation on real Hilbert spaces. We prove that the hypothesis of existence of ordered singular values is fundamental. 相似文献
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María J. Martín 《Journal of Functional Analysis》2006,238(1):298-312
We observe that a formula for the adjoint of a composition operator, known only for special symbols in some spaces of analytic functions, actually holds for every admissible symbol and in any Hilbert space of analytic functions with reproducing kernels. Along with some new results, all known formulas for the adjoint obtained so far follow easily as a consequence, some in an improved form. 相似文献
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In this paper, with the help of spectral integral, we show a quantitative version of the Bishop-Phelps theorem for operators in complex Hilbert spaces. Precisely, let H be a complex Hilbert space and 0 ε 1/2. Then for every bounded linear operator T : H → H and x0 ∈ H with ||T|| = 1 = ||x0|| such that ||Tx0|| 1 ε, there exist xε∈ H and a bounded linear operator S : H → H with||S|| = 1 = ||xε|| such that ||Sxε|| = 1, ||xε-x0|| ≤ (2ε)1/2 + 4(2ε)1/2, ||S-T|| ≤(2ε)1/2. 相似文献
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Petru Cojuhari 《Journal of Mathematical Analysis and Applications》2005,304(2):584-598
We introduce the notion of induced Hilbert spaces for positive unbounded operators and show that the energy spaces associated to several classical boundary value problems for partial differential operators are relevant examples of this type. The main result is a generalization of the Krein-Reid lifting theorem to this unbounded case and we indicate how it provides estimates of the spectra of operators with respect to energy spaces. 相似文献
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In this paper, we study some properties of composition operators on Hilbert spaces of Dirichlet series, which include the Fredholmness, Hilbert-Schmidtness, spectra, cyclic and hypercyclic phenomenons, and also answer a norm question raised by Cowen and MacCluer. 相似文献
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Sign type spectra are an important tool in the investigation of spectral properties of selfadjoint operators in Krein spaces. It is our aim to show that also sign type spectra for normal operators in Krein spaces provide insight in the spectral nature of the operator: If the real part and the imaginary part of a normal operator in a Krein space have real spectra only and if the growth of the resolvent of the imaginary part (close to the real axis) is of finite order, then the normal operator possesses a local spectral function defined for Borel subsets of the spectrum which belong to positive (negative) type spectrum. Moreover, the restriction of the normal operator to the spectral subspace corresponding to such a Borel subset is a normal operator in some Hilbert space. In particular, if the spectrum consists entirely out of positive and negative type spectrum, then the operator is similar to a normal operator in some Hilbert space. We use this result to show the existence of operator roots of a class of quadratic operator polynomials with normal coefficients. 相似文献
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Masoumeh Faghih-Ahmadi Karim Hedayatian 《Journal of Mathematical Analysis and Applications》2022,505(2):125500
Let H be an infinite dimensional complex Hilbert space and T be a bounded linear operator on H. We show that if there exists such that the closure of is H, then there is a subsequence such that the closed linear span of is not the whole space H. 相似文献