Block Operator Matrices

This book will be very useful to senior/graduate and those who are doing research work or intend to work in the area of operator theory. The reader is assumed to know fundamental functional analysis. In this book our aim is to discuss the properties of operator matrix related to the properties of operators used in the entries. For example, we discuss the invertibility of the operator matrix, Fredholmness of the operator matrix, the closedness of the operator matrix, relative boundedness of the operator matrix, compactness and relative compactness of the operator matrix. A quadratic numerical range of an operator matrix is defined and relationship between the spectrum and the classical numerical range of an operator matrix are discussed. At the end of the book we discuss the spectral decomposition of some operator matrices.