Spectral properties of tensor products of linear operators. II. The approximate point spectrum and Kato essential spectrum

Spectrum and essential spectrum of linear combinations of composition operators on the Hardy space H2

Let -----. For an analytic self-map ---  of --- , Let --- be the composition operator with composite map ---  so that ----. Let ---  be a bounded analytic function on --- . The weighted composition operator ---  is defined by --- . Suppose that ---  is the Hardy space, consisting of all analytic functions defined on --- , whose Maclaurin cofficients are square summable. .....

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Spectrum Properties of the Koopman and Frobenius-Perron Operators

Almost multiplicative linear functionals and approximate spectrum

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...

The Spectral Mapping Theorem for Joint Approximate Point Spectrum

The spectral mapping theorem for joint approximate point spectrum is proved when A is an «-tuple of commuting operators on a Banach space and ƒ is any w-tuple of rational functions for which f (A) is defined. The purpose of the paper is to show how properties of parts of the joint spectrum can be obtained by use of spaces of sequences of vectors. The method (first used for general Banach spaces...