Functors on the Category of Hilbert Spaces PDF Download
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Author: Jan Epema
Publisher:
ISBN:
Category : Functor theory
Languages : en
Pages : 132
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Author: Jan Epema
Publisher:
ISBN:
Category : Functor theory
Languages : en
Pages : 132
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Book Description
Author: P.W. Michor
Publisher: Springer
ISBN: 3540358471
Category : Mathematics
Languages : en
Pages : 104
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Author: Jorge-Nuno O. Silva
Publisher: Universal-Publishers
ISBN: 1581120230
Category : Mathematics
Languages : en
Pages : 31
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Book Description
In this work we explore the relation between some local Dirichlet spaces and some operator ranges. As an application we give numerical bounds for an equivalence of norms on a particular subspace of the Hardy space. Based on these results we introduce an operator on H^2 which we study in some detail. We also introduce a Hilbert space of analytic functions on the unit disc, prove the polynomials are dense in it, and give a characterization of its elements. On these spaces we study the action of composition operators induced by holomorphic self maps of the disc. We give characterizations of the bounded and compact ones in terms of the behavior of the inducing maps.
Author: Jan Epema
Publisher:
ISBN:
Category :
Languages : en
Pages : 116
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Author: Emily Riehl
Publisher: Courier Dover Publications
ISBN: 0486820807
Category : Mathematics
Languages : en
Pages : 273
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Book Description
Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.
Author: Chris Heunen
Publisher: Oxford University Press
ISBN: 0191060062
Category : Mathematics
Languages : en
Pages : 320
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Book Description
Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition, and a conceptual way to understand many high-level quantum phenomena. This text lays the foundation for this categorical quantum mechanics, with an emphasis on the graphical calculus which makes computation intuitive. Biproducts and dual objects are introduced and used to model superposition and entanglement, with quantum teleportation studied abstractly using these structures. Monoids, Frobenius structures and Hopf algebras are described, and it is shown how they can be used to model classical information and complementary observables. The CP construction, a categorical tool to describe probabilistic quantum systems, is also investigated. The last chapter introduces higher categories, surface diagrams and 2-Hilbert spaces, and shows how the language of duality in monoidal 2-categories can be used to reason about quantum protocols, including quantum teleportation and dense coding. Prior knowledge of linear algebra, quantum information or category theory would give an ideal background for studying this text, but it is not assumed, with essential background material given in a self-contained introductory chapter. Throughout the text links with many other areas are highlighted, such as representation theory, topology, quantum algebra, knot theory, and probability theory, and nonstandard models are presented, such as sets and relations. All results are stated rigorously, and full proofs are given as far as possible, making this book an invaluable reference for modern techniques in quantum logic, with much of the material not available in any other textbook.
Author: Alain Guichardet
Publisher: Lecture Notes in Mathematics
ISBN:
Category : Mathematics
Languages : en
Pages : 214
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Author: Tom Leinster
Publisher: Cambridge University Press
ISBN: 1108832709
Category : Language Arts & Disciplines
Languages : en
Pages : 457
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Book Description
Discover the mathematical riches of 'what is diversity?' in a book that adds mathematical rigour to a vital ecological debate.
Author: Louis De Branges
Publisher:
ISBN:
Category : Functions, Entire
Languages : en
Pages : 344
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Book Description
Author: Willi-Hans Steeb
Publisher:
ISBN:
Category : Hilbert space
Languages : en
Pages : 208
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Book Description
