In this article, we characterize the sufficient and necessary conditions for positiveness of operator matrices with Toeplitz little Hankel operators on Bergman space. Further, explore some to be normal unitary.

A recent paper of A. Connes and W.D. van Suijlekom [Comm. Math. Phys. 383 (2021), pp. 2021–2067] identifies the operator system n × n\times n</mml:...

Weyl’s theorem for an operator says that the complement in the spectrum of the Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity. H. Weyl ([22]) discovered that this property holds for hermitian operators and it has been extended from hermitian operators to hyponormal operators and to Toeplitz operators by L. Coburn ([5]), and to sever...

We develop a data-sparse and accurate approximation to parabolic solution operators in the case of a rather general elliptic part given by a strongly P-positive operator [4]. In the preceding papers [12]–[17], a class of matrices (H-matrices) has been analysed which are data-sparse and allow an approximate matrix arithmetic with almost linear complexity. In particular, the matrix-vector/matrixm...

Let \(\mathcal {H}\) be a complex Hilbert space and let A positive operator on {H}\). We obtain new bounds for the A-numerical radius of operators in semi-Hilbertian {B}_A(\mathcal {H})\) that generalize improve existing ones. Further, we estimate an upper bound \(\mathbb {A}\)-operator seminorm \(2\times 2\) matrices, where {A}=\text{ diag }(A,A)\). The obtained here generalizes earlier relate...