Operators, Semigroups, Algebras and Function Theory: Volume from IWOTA Lancaster 2021 (Operator Theory: Advances and Applications, 292)

Preface
	Special Sessions
	Main Lectures
	The Proceedings
Contents
Criteria for Eventual Domination of Operator Semigroupsand Resolvents
	1 Introduction
		1.1 Motivation and Context
		1.2 Notation and Terminology
		1.3 Organization of the Article
	2 Eventual Domination of Resolvents
	3 Eventual Domination of Semigroups
	4 Applications
		4.1 The Laplace Operator with Anti-Symmetric Boundary Conditions
		4.2 Laplace Operators with Non-Local Boundary Conditions
		4.3 Dirichlet and Neumann Boundary Conditions: What Is (Eventually) in Between?
		4.4 Bi-Laplace Operator with Wentzell Boundary Conditions
		4.5 Differential Operators of Odd Order
	5 Some Remarks on Eventual Positivity of Cesàro Means
	References
Bounded Functional Calculi for Unbounded Operators
	1 Introduction
	2 Semigroup Generators and Hille-Phillips Calculus
	3 B-Calculus
	4 D- and H-Calculi for Sectorial Operators
	5 Further Extensions on Hilbert Spaces
	References
A Noncommutative Bishop Peak Interpolation-Set Theorem
	1 Introduction
	2 On the `Bishop Peak Interpolation-Set\' Result
	References
Non-autonomous Desch–Schappacher Perturbations
	1 Introduction
	2 Autonomous Systems and C0-Semigroups
		2.1 C0-Semigroups
		2.2 Extrapolation Spaces
		2.3 The Favard Class
	3 Non-autonomous Abstract Cauchy Problems
		3.1 Evolution Families
		3.2 CD-Systems
	4 Non-autonomous Desch–Schappacher Perturbations
		4.1 Perturbations of CD-Systems
		4.2 CD-Systems in Extrapolation Spaces
		4.3 A Non-autonomous Desch–Schappacher Perturbation
	5 Example: Non-autonomous Uniformly Strongly Elliptic Differential Operators
	References
Operator Algebras Associated with Graphs and Categoriesof Paths: A Survey
	1 Introduction
	2 Definitions
	3 Graph C*-Algebras and Free Semigroupoid Algebras
	4 Operator Algebras from Higher Rank Graphs
	5 Operator Algebras from Categories of Paths
	References
Finite Sections of Periodic Schrödinger Operators
	1 Introduction
	2 The FSM: Operators and Tools
		2.1 Band Operators and the FSM
		2.2 Limit Operators
	3 Periodic Schrödinger Operators
		3.1 Trace Condition for the Spectrum of Periodic Schrödinger Operators
		3.2 One-Sided Periodic Schrödinger Operators
		3.3 Periodic Schrödinger Operators with {0,λ}-Valued Potentials
	4 Proofs of Our Main Theorems
		4.1 Proof of Theorem 1.3
		4.2 Proof of Remarks 1.2 and 1.4
		4.3 Systematic Studies of {0,λ}-Valued Potentials
		4.4 Proof of Theorem 1.1
	References
The Jacobi Operator and Its Donoghue m-Functions
	1 Introduction
	2 Some Background
	3 Donoghue m-functions: Two Limit Circle Endpoints
	4 Donoghue m-functions: One Limit Circle Endpoint
	5 The Jacobi Operator and Its Donoghue m-Functions
		5.1 The Regular and Limit Circle Case α, β(-1,1)
		5.2 Precisely One Interval Endpoint in the Limit Point Case
	Appendix A: The Hypergeometric and Jacobi Differential Equations
	Appendix B: Connection Formulas
	Appendix C: Behavior of yj,α,β,1(z,x), j=1,2, near x=1
	References
Entanglement Breaking Rank Via Complementary Channelsand Multiplicative Domains
	1 Introduction
		1.1 Preliminaries
	2 Complementary Channels and a Characterisation of Entanglement Breaking Channels
	3 The Multiplicative Domain of a Completely Positive Map and Entanglement Breaking Rank
	4 Concluding Remarks
	References
On the Bergman Projection and Kernel in Periodic Planar Domains
	1 Introduction
	2 Bergman Kernels and Conformal Mappings on Periodic Domains
	3 Floquet Transform in Bergman Spaces
	4 General Kernel Formula for the Periodic Domain
	5 Weights, Domains and Projections
	6 Simply Connected Periodic Domain
	7 Applications
	References
Brown Measure of R-diagonal Operators, Revisited
	1 Introduction
	2 Preliminaries and Notations
	3 The Subordinations and Haagerup–Schultz\'s Approach
	4 The Brown Measure of R-diagonal Operators
	5 An Alternative Proof for the Brown Measure Formula
	6 Freeness with Amalgamation and R-diagonal Operators
	7 Some Miscellaneous Applications
	References