Page 349 - DMTH505_MEASURE_THEOREY_AND_FUNCTIONAL_ANALYSIS
P. 349
Measure Theory and Functional Analysis
Notes 31.4 Review Questions
1. If T (H) is a self-adjoint operator, then (T) = {m, M} where m, M are spectral values.
2. If T is self-adjoint operator then (T) is the subset of the real line [– T , T ].
–1
3. Let R (T) = (T – I) for a T B (X, X). Prove that R T 0 as .
4. Prove that the projection of a Hilbert space H onto a finite dimensional subspace of H is
compact.
31.5 Further Readings
Books Walter Rudin, Real and complex analysis, Third, McGraw-Hill Book Co., New York,
1987.
Erwin Kreyszig, Introductory functional analysis with applications, John Wiley &
Sons Inc., New York, 1989.
Online links www.math.washington.edu
chicago.academia.edu
www.math.ethz.ch/~ Kowalski/spectral-theory.pdf
342 LOVELY PROFESSIONAL UNIVERSITY
