Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras 论文

摘要

Let A be a bounded operator on a Banach space X. Ascalarλis in the spectrum of A if the operator A − λ is not invertible. Case closed. What more is there to say? As anyone with the slightest exposure to operator theory will testify, there is so much out there that no book could come close to being comprehensive. What authors do in such situations is choose a small area or topic of interest to the author and concentrate on that. The present book is no exception. The spectral theory of operators has its roots in the theory of matrices and in the theory of integral equations. In the early years of matrix theory, the terms “proper value”, “characteristic value”, “secular value”, and “latent root ” were all used for what we now call an eigenvalue. Laguerre constructed the exponential function of a matrix, and Frobenius obtained expansions for the resolvent operator in the neighborhood of a pole. Sylvester constructed arbitrary functions of a matrix with distinct eigenvalues. This was generalized by Buchheim to the case of multiple eigenvalues. It was F. Reisz who extended these concepts to the space l2. Dealing with compact