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This book tours the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, along with some of their main applications. It requires only a basicMoreThis book tours the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, along with some of their main applications. It requires only a basic background in functional analysis. The presentation is self-contained and paced appropriately for graduate students new to the subject. Experts will appreciate how the author illustrates the power of methods he has developed with new and simpler proofs of some of the major results in the area, many of which have not appeared earlier in the literature.

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In functional analysis , a discipline within mathematics, an operator space is a Banach space "given together with an isometric embedding into the space B H of all bounded operators on a Hilbert space H. The category of operator spaces includes operator systems and operator algebras. For operator systems, in addition to an induced matrix norm of an operator space, one also has an induced matrix order. For operator algebras, there is still the additional ring structure. From Wikipedia, the free encyclopedia. Introduction to Operator Space Theory. Cambridge University Press.

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Paulsen Published Mathematics. View PDF.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs and how to get involved. Comments: 19 pages. Revised version. OA ; Functional Analysis math.

In this chapter, we first prove a fundamental criterion for an operator between Banach spaces to factor through a Hilbert space. Then we turn to the notion of complete boundedness which is crucial for these notes. In this viewpoint, the underlying idea is the same in both cases completely bounded maps or operators factoring through Hilbert space. At the end of this chapter, we give several examples of bounded linear maps which are not completely bounded, and related norm estimates.

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