The boundedness and compactness of weighted composition operators on the Hardy space H of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function. Schattenclass membership is also considered; as a result, stronger forms of the two main results of a recent paper of Gunatillake are derived. Finally, weighted composition operators on w...

Suppose that m,n ∈ N and that A : R → R is a linear operator. It is shown here that if k, r ∈ N satisfy k < r 6 rank(A) then there exists a subset σ ⊆ {1, . . . ,m} with |σ| = k such that the restriction of A to R ⊆ R is invertible, and moreover the operator norm of the inverse A−1 : A(R) → R is at most a constant multiple of the quantity √ mr/((r − k) ∑m i=r si(A) 2), where s1(A) > . . . > sm(...

In this work we study a class of anharmonic oscillators within the framework Weyl-Hörmander calculus. A prototype is an operator on R n form ( ? ? ) ? + | x 2 k for , integers ?1. We obtain spectral properties in terms Schatten-von Neumann classes their negative powers and derive from them estimates rate growth eigenvalues oscillator . particular give simple proof main term asymptotics these op...

By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.

in this paper we define an order structure on the $p$-operator projective tensor product of herz algebras and we show that the canonical isometric isomorphism between $a_p(gtimes h)$ and $a_p(g)widehat{otimes}^p a_p(h)$ is an order isomorphism for amenable groups $g$ and $h$.

We generalize the theorems of Stein–Tomas and Strichartz about surface restrictions of Fourier transforms to systems of orthonormal functions with an optimal dependence on the number of functions. We deduce the corresponding Strichartz bounds for solutions to Schrödinger equations up to the endpoint, thereby solving an open problem of Frank, Lewin, Lieb and Seiringer. We also prove uniform Sobo...