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An operator-theoretic approach to truncated moment problems

Raúl Curto (1997)

Banach Center Publications

We survey recent developments in operator theory and moment problems, beginning with the study of quadratic hyponormality for unilateral weighted shifts, its connections with truncated Hamburger, Stieltjes, Hausdorff and Toeplitz moment problems, and the subsequent proof that polynomially hyponormal operators need not be subnormal. We present a general elementary approach to truncated moment problems in one or several real or complex variables, based on matrix positivity and extension. Together...

An overview of some recent developments on the Invariant Subspace Problem

Isabelle Chalendar, Jonathan R. Partington (2013)

Concrete Operators

This paper presents an account of some recent approaches to the Invariant Subspace Problem. It contains a brief historical account of the problem, and some more detailed discussions of specific topics, namely, universal operators, the Bishop operators, and Read’s Banach space counter-example involving a finitely strictly singular operator.

Anisotropic Besov spaces and approximation numbers of traces on related fractal sets.

Erika Tamási (2006)

Revista Matemática Complutense

This paper deals with approximation numbers of the compact trace operator of an anisotropic Besov space into some Lp-space,trΓ: Bpps,a (Rn) → Lp(Γ), s > 0, 1 < p < ∞,where Γ is an anisotropic d-set, 0 < d < n. We also prove homogeneity estimates, a homogeneous equivalent norm and the localization property in Bpps,a.

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