{"product_id":"similarity-problems-and-completely-bounded-maps-lecture-notes","title":"Similarity Problems and Completely Bounded Maps - Lecture Notes","description":"\u003cp\u003eIn this review of Similarity Problems and Completely Bounded Maps readers will find a focused, technical introduction to three classic similarity problems within the operator algebra setting. The notes are aimed at graduate students and researchers who want a compact, rigorous treatment that ties group representations, C-algebras, and the disc algebra together through the unifying concept of \u003cstrong\u003ecomplete boundedness\u003c\/strong\u003e. The single biggest reason to buy is the clear assembly of background, partial solutions and key counterexamples that make further study or research accessible.\u003c\/p\u003e\u003ch2\u003eKey Features\u003c\/h2\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eThree related problems:\u003c\/strong\u003e Presents the similarity questions for group representations, C -algebras and the disc algebra so readers can compare approaches across contexts.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eFocused background:\u003c\/strong\u003e Collects the necessary operator theory preliminaries to approach the problems without needing many external sources.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eComplete boundedness emphasis:\u003c\/strong\u003e Uses the key concept of complete boundedness to place disparate problems in a common framework for clearer conceptual understanding.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eExamples and counterexamples:\u003c\/strong\u003e Includes concrete counterexamples and extensions that illuminate the limits of known solutions and guide further inquiry.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eConcise lecture-note format:\u003c\/strong\u003e Delivers material in a compact, readable form appropriate for course use or individual study.\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch2\u003eWho It's For\u003c\/h2\u003e\u003cp\u003eThis volume is best for graduate students in functional analysis, early-career researchers in operator algebras, and instructors looking for a compact set of lecture notes on similarity problems and completely bounded maps. The text assumes familiarity with basic Hilbert space theory and operator algebras and benefits those preparing to read more advanced research papers.\u003c\/p\u003e\u003cp\u003eThose seeking an introductory textbook with extensive exercises or a broad survey of all operator algebra topics should look elsewhere; this is a specialized lecture-note treatment rather than a general textbook. It is not intended as a self-contained primer for readers without prior exposure to B(H) and C -algebras.\u003c\/p\u003e\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eConcise synthesis of three related similarity problems provides a clear research-oriented narrative.\u003c\/li\u003e\n\u003cli\u003eStrong focus on \u003cstrong\u003ecomplete boundedness\u003c\/strong\u003e helps unify different operator algebra contexts.\u003c\/li\u003e\n\u003cli\u003eIncludes helpful examples, counterexamples and extensions that clarify the boundaries of known results.\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\u003cli\u003eLimited exercises and pedagogical scaffolding make it less suitable as a first textbook for beginners.\u003c\/li\u003e\u003c\/ul\u003e\u003ch2\u003eSpecifications\u003c\/h2\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eSimilarity Problems and Completely Bounded Maps\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSeries\u003c\/td\u003e\n\u003ctd\u003eLecture Notes in Mathematics, 1618\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthor\u003c\/td\u003e\n\u003ctd\u003eGilles Pisier\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSubject focus\u003c\/td\u003e\n\u003ctd\u003eOperator algebras, similarity problems, complete boundedness\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eMathematical context\u003c\/td\u003e\n\u003ctd\u003eB(H) bounded operators on a complex Hilbert space\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eKey topics\u003c\/td\u003e\n\u003ctd\u003eGroup representations, C -algebras, disc algebra\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\u003ch2\u003eOur Verdict\u003c\/h2\u003e\u003cp\u003eThese lecture notes are a compact, well-organized resource for readers who already know operator algebra basics and want a targeted treatment of similarity problems framed by \u003cstrong\u003ecomplete boundedness\u003c\/strong\u003e. It is good value for graduate students and researchers seeking concise background, known solutions in special cases, and instructive counterexamples to support further study or research.\u003c\/p\u003e\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\u003cp\u003e\u003cstrong\u003eDoes this book require prior operator algebra knowledge?\u003c\/strong\u003e\u003cbr\u003eYes. Familiarity with Hilbert spaces and basic C -algebra concepts is assumed for full benefit.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAre exercises included for classroom use?\u003c\/strong\u003e\u003cbr\u003eThe notes focus on exposition and examples rather than extensive exercises, so instructors may want to supplement them for coursework.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eDoes it cover solutions to all three problems fully?\u003c\/strong\u003e\u003cbr\u003eIt presents known solutions in special cases and discusses related results and counterexamples, rather than claiming complete general solutions.\u003c\/p\u003e","brand":"Gilles Pisier","offers":[{"title":"Default Title","offer_id":48619022287067,"sku":"3540415246","price":59.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/51IaSyrpgmL._SL1254.jpg?v=1778518549","url":"https:\/\/gearmusthave.com\/products\/similarity-problems-and-completely-bounded-maps-lecture-notes","provider":"GearMustHave","version":"1.0","type":"link"}