| Lerninhalte |
<div> </div><div style="box-sizing: border-box; caret-color: #373a3c; color: #373a3c; font-family: MetaWebPro, sans-serif; font-size: 15px; background-color: #ffffff;">Based on the book "A short course on spectral theory" by William Arveson, the seminar presents the basic tools of modern analysis within the context of what might be called the fundamental problem of operator theory: to calculate spectra of specific operators on infinite-dimensional spaces, especially operators on Hilbert spaces. The notion of spectrum of an operator is based on the more abstract notion of the spectrum of an element of a complex Banach algebra. After working out these fundamentals we turn to more concrete problems of computing spectra of operators of various types. For normal operators, this amounts to a treatment of the spectral theorem. We will present several applications. We finish with the seminar with the special case of the spectral theorem for compact operators.</div> |
eG