Basic theory orientations and c products authors alfsen erik m shultz frederik w focusing on the theory of state spaces of c algebras and von neumann algebras explains how the oriented state space geometrically determines the algebrathe theory of operator algebras was initially motivated by applications to physics but has recently found unexpected new applications to fields . The topic of this book is the theory of state spaces of operator algebras and their geometry the states are of interest because they determine representations of the algebra and its algebraic structure is in an intriguing and fascinating fashion encoded in the geometry of the state space from the beginning the theory of operator algebras was motivated by applications to physics but . Geometry of state spaces of operator algebras mathematics theory applications erik m alfsen frederic w shultz this monograph presents a complete and self contained solution to the long standing problem of giving a geometric description of state spaces of c algebras and von neumann algebras and of their jordan algebraic analogs jb algebras and jbw algebras. Operator algebras come in two varieties c algebras and von neumann algebras my friends who work in the non self adjoint theory will forgive me for using the term in this way for the purposes of this review concretely a c algebra is a linear subspace of bh the space of bounded operators on a complex hilbert space h which is algebraically closed under operator products and adjoints . Stanford libraries official online search tool for books media journals databases government documents and more
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