Basic properties of Davis-Wielandt shells are presented. Conditions on two operators A and B with the same Davis-Wielandt shells are analyzed. Special attention is given to the case when B is a compression of A, and when B = A∗, A, or (A∗)t, where A is the transpose of A with respect to an orthonormal basis. The results are used to study the point spectrum, approximate spectrum, and residual sp...

Recently some important results have been proved showing that the gap between the largest eigenvalue A: of a finite regular graph of valency k and its second eigenvalue is related to expansion properties of the graph [1]. In this paper we investigate infinite graphs and show that in this case the expansion properties are related to the spectral radius of the graph. First we introduce necessary ...

By a famous result, functions in backward shift invariant subspaces in Hardy spaces are characterized by the fact that they admit a pseudocontinuation a.e. on T. More can be said if the spectrum of the associated inner function has holes on T. Then the functions of the invariant subspaces even extend analytically through these holes. We will discuss the situation in weighted backward shift inva...

Let H be an infinite-dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H. In this paper, we characterized maps ϕ:B(H)→B(H), which are surjective up to compact preserving set left semi-Weyl in both directions. As application, proved that ϕ preserves essential approximate point spectrum if only ideal is invariant under induced map φ Calkin automor...