Birkhoff cones, symbolic dynamics and spectrum of transfer operators

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...

Approximation of nonessential spectrum of transfer operators

We give suucient conditions to approximate the \nonessential" spectrum of a bounded operator L acting on a Banach space B by part of the spectra of a sequence of compact (or nite rank) operators L j = (Id ? j)L(Id ? j), where Id ? j is a suitable family of uniformly bounded operators which approach the identity. (By nonessential spectrum we mean here all the spectrum outside of the disc of radi...

Stability of the spectrum for transfer operators

We prove stability of the isolated eigenvalues of transfer operators satisfying a Lasota-Yorke type inequality under a broad class of random and nonrandom perturbations including Ulam-type discretizations. The results are formulated in an abstract framework.

Spectrum Properties of the Koopman and Frobenius-Perron Operators

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. .....