A generalization of the Aleksandrov operator is provided, in order to represent the adjoint of a weighted composition operator on H2 by means of an integral with respect to a measure. In particular, we show the existence of a family of measures which represents the adjoint of a weighted composition operator under fairly mild assumptions, and we discuss not only uniqueness but also the generaliz...

We explicitly determine the spectrum of transfer operators (acting on spaces of holomorphic functions) associated to analytic expanding circle maps arising from finite Blaschke products. This is achieved by deriving a convenient natural representation of the respective adjoint operators.

In Noncommutative Geometry, as in quantum theory, classically real variables are assumed to correspond to self-adjoint operators. We consider the relaxation of the requirement of self-adjointness to mere symmetry for operators Xi which encode space-time information.

This paper deals with local spectral properties of Extended Hamilton operators and their adjoint operators. The relationship between the (strongly decomposability, hyperinvariant subspace problem, etc.) corresponding is obtained.

These are notes from two lectures given in MATH 27200, Basic Functional Analysis, at the University of Chicago in March 2010. The proof of the spectral theorem for compact operators comes from [Zim90, Chapter 3]. 1. The Spectral Theorem for Compact Operators The idea of the proof of the spectral theorem for compact self-adjoint operators on a Hilbert space is very similar to the finite-dimensio...

For a class of singular potentials, including the Coulomb potential and V (x) = g/x with the coefficient g in a certain range, the corresponding Schrödinger operator is not automatically self-adjoint on its natural domain. Such operators admit more than one self-adjoint domain, and the spectrum and all physical consequences depend seriously on the selfadjoint version chosen. The talk discusses ...

We present a new necessary condition for similarity of indefinite Sturm-Liouville operators to self-adjoint operators. This condition is formulated in terms of Weyl-Titchmarsh m-functions. Also we obtain necessary conditions for regularity of the critical points 0 and∞ of J-nonnegative Sturm-Liouville operators. Using this result, we construct several examples of operators with the singular cri...

Adjoint triples are an interesting generalization of t-norms and their residuated implications, since they increase the flexibility in the framework where they are used. Following the same motivation of adjoint triples, in order to reduce the mathematical requirements for the computation, extended-order algebras are studied. Extended-order algebras are implicative algebras that generalize the i...

We discuss several natural metrics on spaces of unbounded self– adjoint operators and their relations, among them the Riesz and the graph metric. We show that the topologies of the spaces of Fredholm operators resp. invertible operators depend heavily on the metric. Nevertheless we prove that in all cases the spectral flow is up to a normalization the only integer invariant of paths which is pa...