Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*-algebra rather than the field of complex numbers. This theory has prove to be a convenient tool in the theory of operator algebras, allowing to study C*-algebras by studying Hilbert C*-modules over them. Thus, the theory of Hilbert C*-modules is an important tool for studying Morita equivalence of C*-algebras and its application to group representation theory and crossed product C*-algebras, K-theory and KK-theory of operator algebras, completely positive maps between C*-algebras, unbounded operators and quantum groups, vector bundles, noncommutative geometry, mathematical and theoretical physics. Beside these, theory of Hilbert C*-modules is very interesting on it\u2019s own. Locally C*-algebras are generalizations of C*-algebras. Instead of being given by a single C*-norm, the topology of a locally C*-algebra is defined by a directed family of C*-seminorms. Such many concepts as Hilbert C*-module, adjointable operator, compact operator, (induced) representation, strong Morita equivalence can be defined with obvious modifications in the framework of locally C*-algebras. Most of the basic properties of Hilbert C*-modules are still valid for Hilbert modules over locally C*-algebras, but the proofs are not always straightforward. This book is an introduction in theory of Hilbert modules over locally C*-algebras. The author did not purpose to discuss here all aspects of Hilbert modules over locally C*-algebras, but she has tried to explain the basic notions and theorems of this theory, a number important of examples and some results about representations of locally C*-algebras. A significant part of the results presented here was obtained by the author. The detailed bibliography of theory of Hilbert C*-modules can be found in Hilbert C*-Modules Homepage.<\/p>\n","protected":false},"excerpt":{"rendered":"
Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*-algebra rather than the field of complex numbers. This theory has prove to be a convenient tool in the theory of operator algebras, allowing to study C*-algebras by studying Hilbert C*-modules over them. Thus, the theory of Hilbert […]<\/p>\n","protected":false},"featured_media":8906,"comment_status":"open","ping_status":"closed","template":"","meta":[],"product_brand":[],"product_cat":[982,986],"product_tag":[898],"class_list":{"0":"post-5187","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-stiinte-exacte","7":"product_cat-matematica","8":"product_tag-matematica","10":"first","11":"instock","12":"shipping-taxable","13":"purchasable","14":"product-type-simple"},"_links":{"self":[{"href":"https:\/\/editura-unibuc.ro\/en\/wp-json\/wp\/v2\/product\/5187","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/editura-unibuc.ro\/en\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/editura-unibuc.ro\/en\/wp-json\/wp\/v2\/types\/product"}],"replies":[{"embeddable":true,"href":"https:\/\/editura-unibuc.ro\/en\/wp-json\/wp\/v2\/comments?post=5187"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/editura-unibuc.ro\/en\/wp-json\/wp\/v2\/media\/8906"}],"wp:attachment":[{"href":"https:\/\/editura-unibuc.ro\/en\/wp-json\/wp\/v2\/media?parent=5187"}],"wp:term":[{"taxonomy":"product_brand","embeddable":true,"href":"https:\/\/editura-unibuc.ro\/en\/wp-json\/wp\/v2\/product_brand?post=5187"},{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/editura-unibuc.ro\/en\/wp-json\/wp\/v2\/product_cat?post=5187"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/editura-unibuc.ro\/en\/wp-json\/wp\/v2\/product_tag?post=5187"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}