Schur multipliers and operator-valued Foguel-Hankel operators

广义Foguel-汉克尔算子

Generalized Foguel-Hankel Operators

本文提出广义Foguel-汉克尔算子，探讨其幂有界性与收缩相似性条件的关系，揭示了希尔伯特矩阵下的等价条件。

类似收缩算子的Foguel型算子

Foguel-type operators similar to contractions

本文研究了七种Foguel型算子，通过特征化证明它们均与收缩算子相似。

A Note on the Norm and Spectrum of a Foguel Operator

We present two ways to compute the norm of a Foguel operator. One of these is algebraic and the other makes use of the Schur complement. This gives a two simpler proof of a result of Garcia. We also provide an extension of these results.

Hankel and Toeplitz-Schur Multipliers

We study the problem of characterizing Hankel-Schur multipliers and Toeplitz-Schur multipliers of Schatten-von Neumann class $\bS_p$ for $0<p<1$. We obtain various sharp necessary conditions and sufficient conditions for a Hankel matrix to be a Schur multiplier of $\bS_p$. We also give a characterization of the Hankel-Schur multipliers of $\bS_p$ whose symbols have lacunary power series. Then the results on Hankel-Schur multipliers are used to obtain a characterization of the Toeplitz-Schur multipliers of $\bS_p$. Finally, we return to Hankel-Schur multipliers and obtain new results in the cas…

Schur-Nevanlinna parameters, Riesz bases, and compact Hankel operators on the model space

We study Riesz bases/Riesz sequences of reproducing kernels in the model space $K_θ$ in connection with the corresponding Schur--Nevanlinna parameters and functions. In particular, we construct inner functions with given Schur--Nevanlinna parameters at a given sequence $Λ$ such that the corresponding systems of projections of reproducing kernels in the model space are complete/non complete. Furthermore, we give a compactness criterion for Hankel operators with symbol $θ\overline B$, where $θ$ is an inner function and $B$ is an interpolating Blaschke product and use this criterion to describe R…

Paley's theorem for Hankel matrices via the Schur test

Paley's theorem about lacunary coefficients of functions in the classical space $H^1$ on the unit circle is equivalent to the statement that certain Hankel matrices define bounded operators on $\ell^2$ of the nonnegative integers. Since that statement reduces easily to the case where the entries in the matrix are all nonnegative, it must be provable by the Schur test. We give such proofs with interesting patterns in the vectors used in the test, and we recover the best constant in the main case. We use related ideas to reprove the characterization of Paley multipliers from $H^1$ to $H^2$.