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A Primer on Hilbert Space Operators / von Piotr Sołtan

The book contains a concise presentation of fundamental aspects of the theory of operators on Hilbert spaces. Among topics covered are functional calculus and spectral theorems, compact operators, trace class and Hilbert-Schmidt operators, self-adjoint extensions of symmetric operators, and one-parameter groups of operators.

The exposition of material on unbounded operators is based on a novel tool, the so called z-transform, which provides a way to encode full information about unbounded operators in bounded ones, hence making many technical aspects of the theory less involved.