Topological Algebras with InvolutionThis book familiarizes both popular and fundamental notions and techniques from the theory of non-normed topological algebras with involution, demonstrating with examples and basic results the necessity of this perspective. The main body of the book is focussed on the Hilbert-space (bounded) representation theory of topological *-algebras and their topological tensor products, since in our physical world, apart from the majority of the existing unbounded operators, we often meet operators that are forced to be bounded, like in the case of symmetric *-algebras. So, one gets an account of how things behave, when the mathematical structures are far from being algebras endowed with a complete or non-complete algebra norm. In problems related with mathematical physics, such instances are, indeed, quite common. Key features: - Lucid presentation- Smooth in reading- Informative- Illustrated by examples- Familiarizes the reader with the non-normed *-world- Encourages the hesitant- Welcomes new comers. |
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0-neighborhood 2nd countable A[TA A[TT A₁ advertibly complete AÔB Arens-Michael algebra B[TB C*-enveloping algebra C*-seminorm Cc(X clearly continuous linear form continuous positive linear Corollary corresponding defined Definition denoted element enveloping locally C*-algebra equicontinuous Example finite following statements Fréchet algebra Fréchet locally convex Gel'fand Hausdorff Hence hermitian Hilbert space homeomorphism implies instance inverse limit inverse limit preserving involutive algebra involutive Arens-Michael L¹(G Lemma Let A[Tr locally compact locally convex algebra locally convex spaces locally equicontinuous m-barrelled m-convex m-norm m*-convex algebra moreover morphism non-normed nonzero normed algebra PA(x positive linear form Proof Proposition proved Q-algebra quotient ra(x representation result sb-algebra Section seminorm semisimple SPA(x spectral radius spectrum statements are equivalent subalgebra tensor product tensorial topology Theorem topological algebra topological algebra A[7 topological isomorphism topologically irreducible unique unital commutative
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Page iv - Hence, he said in answer to Zeno, motion is not, like counting, a discrete operation, a series of jerks : the moved thing does not stop at the stages which the calculator chooses to make. The interest which Aristotle took in these inquiries accounts for the fact that the sole extant Greek...
Page xv - Studies wishes to acknowledge its indebtedness and express its deep gratitude to all those who in one way or another contributed to the...
References to this book
Function Spaces: Fifth Conference on Function Spaces, May 16-20, 2006 ... Krzysztof Jarosz No preview available - 2007 |