On the Weyl Spectrum: Spectral Mapping Theorem and Weyl's Theorem

A note on spectral mapping theorem

This paper aims to present the well-known spectral mapping theorem for multi-variable functions.

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...

Weyl Spectra and Weyl’s Theorem

“Weyl’s theorem” for an operator on a Hilbert space is a statement that the complement in the spectrum of the “Weyl spectrum” coincides with the isolated eigenvalues of finite multiplicity. In this paper we consider how Weyl’s theorem survives for polynomials of operators and under quasinilpotent or compact perturbations. First, we show that if T is reduced by each of its finite-dimensional eig...

The Peter-Weyl Theorem and Generalizations

The Weyl Inequality and Sárközy’s Theorem

A Weyl sum is an exponential sum of the form (1) S = N n=1 e 2πiP (n) where P (x) is a polynomial with real coefficients. The purpose of this section is to derive Weyl's estimates for these sums in the special case when P (x) = αx 2 .