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This book is a tribute to the achievements of Ilya Spitkovsky in operator theory, pseudo-differential and integral equations, factorization theory and many other related topics. Ilya Spitkovsky started his career under the guidance of Mark Krein in Odessa, Ukraine. During these years, Ilya’s rigorous and clear style of doing mathematics matured. Since 1990 Ilya Spitkovsky has been a professor of mathematics at the College of William and Mary in Williamsburg, Virginia, where he has taught a wide range of courses, including linear algebra, real, complex, and functional analysis. He has authored more than 300 publications, including four research monographs, and edited eight books of proceedings. Ilya Spitkovsky is currently a member of the editorial board of five international journals. Since 2013 he is a professor of the Division of Science and Mathematics New York University Abu Dhabi, UAE. With this volume, the authors of the articles join the large family of people who congratulate Ilya Spitkovsky on his anniversary. It is their wish that the contributions in this volume offer inspiring insights to researchers working in these fields.

Operator theory. --- Operator Theory.

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The first edition of this book appeared in 1981 as a direct continuation of Lectures of von Neumann Algebras (by Ş.V. Strătilă and L. Zsidó) and, until 2003, was the only comprehensive monograph on the subject. Addressing the students of mathematics and physics and researchers interested in operator algebras, noncommutative geometry and free probability, this revised edition covers the fundamentals and latest developments in the field of operator algebras. It discusses the group-measure space construction, Krieger factors, infinite tensor products of factors of type I (ITPFI factors) and construction of the type III_1 hyperfinite factor. It also studies the techniques necessary for continuous and discrete decomposition, duality theory for noncommutative groups, discrete decomposition of Connes, and Ocneanu's result on the actions of amenable groups. It contains a detailed consideration of groups of automorphisms and their spectral theory, and the theory of crossed products.

Operator algebras.

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This volume contains the proceedings of a three day mini-conference on operator theory and partial differential equations held at Macquarie University in September 1986, under the sponsorship of the Centre for Mathematical Analysis (Australian National University) whose financial assistance is gratefully acknowledged. It is divided into two parts.

Operator theory

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This book introduces several powerful techniques and fundamental ideas involving block matrices of operators, as well as matrices with elements in a C*-algebra. These techniques allow for the solution of problems that may be difficult to treat. Specifically, 2×2 operator matrices yield significant mathematical inequalities in various fields of operator theory and matrix analysis. The authors employ block matrices to simplify complicated problems. Operator matrices have garnered attention for their applications in quantum information and computing theories. Each chapter concludes with a diverse set of exercises and problems for readers, along with references to relevant literature. Some problems pose open questions, while others challenge readers and provide suggestions for future research. This book is suitable for an advanced undergraduate or graduate course and can be used in the classroom. It also serves as a valuable resource for researchers and students in mathematics and physics who have a basic understanding of linear algebra, functional analysis, and operator theory.

Operator theory. --- Operator Theory. --- Matrices.

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This volume is dedicated to Rien Kaashoek on the occasion of his 80th birthday and celebrates his many contributions to the field of operator theory during more than fifty years. In the first part of the volume, biographical information and personal accounts on the life of Rien Kaashoek are presented. Eighteen research papers by friends and colleagues of Rien Kaashoek are included in the second part. Contributions by J. Agler, Z.A. Lykova, N.J. Young, J.A. Ball, G.J. Groenewald, S. ter Horst, H. Bart, T. Ehrhardt, B. Silbermann, J.M. Bogoya, S.M. Grudsky, I.S. Malysheva, A. Böttcher, E. Wegert, Z. Zhou, Y. Eidelman, I. Haimovici, A.E. Frazho, A.C.M. Ran, B. Fritzsche, B. Kirstein, C.Madler, J. J. Jaftha, D.B. Janse van Rensburg, P. Junghanns, R. Kaiser, J. Nemcova, M. Petreczky, J.H. van Schuppen, L. Plevnik, P. Semrl, A. Sakhnovich, F.-O. Speck, S. Sremac, H.J. Woerdeman, H. Wolkowicz and N. Vasilevski.

Operator theory. --- Operator Theory. --- Functional analysis --- Operator theory