Operator Theory

Operator theory is a very wide field, with numerous facets, both applied and theoretical. In this book we focus on the study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). There are deep connections with complex analysis, functional analysis, mathematical physics, electrical engineering, machine learning and physics to name a few. Fascinating new directions and connections regularly appear, such as operator spaces, free probability, and applications to hypercomplex analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and we hope you enjoy the reading, and profit from this endeavor.

• Multivariable operator theory
• Superoscillations
• Quaternionic and Clifford operator theory
• Function spaces of holomorphic and hyperholomorphic functions
• Linear systems
• Schur analysis
• de Branges spaces
• Indefinite inner product spaces
• Infinite dimensional analysis
• Noncommutative analysis
• Reproducing kernel Hilbert spaces

• Ben-Gurion University of the Negev, Department of Mathematics, Beer-Sheva, Israel

  Daniel Alpay

• Daniel Alpay, Schmidt College of Science and Technology, Chapman University, Orange, CA, USA
• Fabrizio Colombo, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy
• Irene Sabadini, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy

• Anton Baranov, Department of Mathematics and Mechanics, St. Petersburg State University, Pedrodvorets, Russia
• Kirill Cherednichenko, University of Bath, Bath, UK
  
• Elena Cherkaev, Department of Mathematics, University of Utah, Salt Lake City, Utah, USA
• Michele Correggi, Politecnico di Milano, Milan, Italy
  
• Raul Curto,University of Iowa, Iowa City, Iowa, USA
• Ilan Hirshberg, Ben Gurion University, Beersheba, Israel
  
• Palle E.T. Jorgensen, Department of Mathematics, The University of Iowa, Iowa City, IA, USA
• Matthias Langer, Department of Mathematics and Statistics, University of Strathclyde, Glasgow, Scotland, UK 
• Javad Mashreghi, Université Laval Canada, Quebec City, Quebec, Canada
• Mamadou Mboup, Université de Reims Champagne Ardenne, CReSTIC - UFR des Sciences Exactes et Naturelles Moulin de la Housse, Reims, France
• Scott McCullogh,University of Florida, Gainesville, FL, USA
  
• Mihai Putinar, UC Santa Barbara, Santa Barbara, CA, USA
• Orr Shalit, Technion Israel of Technology, Haifa, Israel
  
• Daniele C. Struppa, Schmid College of Science and Technology, Chapman University, Orange, CA, USA
  
• Franciszek Hugon Szafraniec, Instytut Matematyki, Uniwersytet Jagiellónski, Kraków, Poland
  
• Michal Wojtylak, Jagellonian University, Krakow, Poland
  
• Harald Woracek, Institut for Analysis and Scientific Computing, Vienna University of Technology, Vienna, Austria

Prof. Daniel Alpay is a faculty member of the Schmid College of Science and Technology at Chapman University, United States. He holds the Foster G. and Mary McGaw Professorship in Mathematical Sciences. He has a double formation of electrical engineer (Telecom Paris, graduated 1978) and mathematician (PhD, Weizmann Institute, 1986). His research includes operator theory, stochastic analysis, and the theory of linear systems. Together with co-authors, he has written 10 books and more than 310 research papers, and edited 18 books.

Prof. Fabrizio Colombo is a faculty member of the Department of Mathematics at Politecnico di Milano. He has the PhD in Mathematics (Università Statale di Milano, 1997). His research interest include operator theory, spectral theory on the S-spectrum, hypercomplex analysis and the theory of superoscillations. Together with co-authors, he has written 9 books and over 230 research papers. He is editor in some mathematical journals. 

Prof. Irene Sabadini is a faculty of the Department of Mathematics at Politecnico di Milano. She has the PhD in Mathematics (Università Statale di Milano, 1996). Her research includes the algebraic analysis of Dirac and generalized Cauchy-Riemann operators over noncommutative algebras, complex and hypercomplex analysis. She is co-author of about 220 papers, 8 books, co-editor of 12 volumes and various journals.

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