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...gical]] [[Hausdorff space]], such that each fiber has the structure of a [[Banach space]]. ...jection]], such that each '''fiber''' <math>B_x := \pi^{-1}(x)</math> is a Banach space. Which satisfies the following conditions: ...

...n theorem''' states that if <math> V </math> is a [[left module]] over a [[Banach algebra]] <math> B </math> with a left approximate unit <math> (u_{i})_{i \ |title = Factorization in group algebras ...

...are determined to a large extent by their projections. The idea behind AW*-algebras is to forgot the former, topological, condition, and use only the latter, a Hence an AW*-algebra is a C*-algebras that is at the same time a [[Baer *-ring]]. ...

...is the case where <math>\mathcal{A}</math> is a [[Banach algebra#Banach *-algebras|complete normed *-algebra]]. This algebra satisfies the C*-identity (<math> ...[Normal element|normal]] element. Then, <math>a</math> is unitary if the [[Banach algebra#Spectral theory|spectrum]] <math>\sigma(a)</math> consists only of ...

...is the case where <math>\mathcal{A}</math> is a [[Banach algebra#Banach *-algebras|complete normed *-algebra]], that satisfies the C*-identity (<math>\left\| ...al element, then for every [[continuous function]] <math>f</math> on the [[Banach algebra#Spectral theory|spectrum]] of <math>a</math> the [[continuous funct ...

==Banach algebra structure== ...ary [[Banach algebra]]. Also, {{math|''A''('''T''')}} is isomorphic to the Banach algebra {{math|''l''₁('''Z''')}}, with the isomorphism given by ...

...is the case where <math>\mathcal{A}</math> is a [[Banach algebra#Banach *-algebras|complete normed *-algebra]], that satisfies the C*-identity (<math>\left\| ...<math>f \geq 0</math> which is [[Continuous function|continuous]] on the [[Banach algebra#Spectral theory|spectrum]] of <math>a</math> the [[continuous funct ...

...functions on <math>X.</math> The space <math>\mathcal{C}(X)</math> is a [[Banach algebra]] with respect to this norm.{{harv|Rudin|1973|loc=§11.3}} ...ce, with the norm given by the [[total variation]] of a measure, is also a Banach space belonging to the class of [[ba space]]s. {{harv|Dunford|Schwartz|1958 ...

...the [[holomorphic functional calculus]]. Hypercomplex analysis on Banach algebras is called [[functional analysis]]. ...

.../2800760 }}</ref> Pointwise multiplication gives them the structure of a [[Banach algebra]], and in fact they are the standard examples of abelian [[Von Neum <math> \ell^\infty</math> is a standard example of a [[Banach space]]. In fact, <math>\ell^\infty</math> can be considered as the [[Seque ...

...ub> a quasi-Banach operator ideal, that is an ideal that is also a [[quasi-Banach space]]. [[Category:Operator algebras]] ...

...st = Robert S. |author2=Victor A. Belfi | title = Characterizations of C*-Algebras: The Gelfand–Naimark Theorems | publisher = Marcel Dekker | location = New ...=B. |author2=H. A. Dye |year=1966|title=A Note on Unitary Operators in C*-Algebras |journal=Duke Mathematical Journal |volume=33 |pages=413–416 |doi=10.1215/S ...

...y, <math>X/U</math> is a [[Banach space]], and it is called the ''quotient Banach space'' of <math>X</math> by <math>U</math>). The system of natural mapping ...isms in the category <math>\text{LCS}</math> of locally convex topological algebras. ...

...ixed point algebra under a period two *-anti-automorphism. Jordan operator algebras have been applied in [[quantum mechanics]] and in [[complex geometry]], whe ===Jordan Banach algebra=== ...

==Associative division algebras== ...enius theorem]] states that [[up to]] [[isomorphism]] there are three such algebras: the reals themselves (dimension 1), the field of [[complex number]]s (dime ...

...of a vector space is the field of real numbers or that of complex numbers. Algebras are not assumed to be unital. See also: [[List of Banach spaces]], [[glossary of real and complex analysis]]. ...

...incide with the weak topology of Φ(''A'') obtained from its norm-dual as a Banach space. ...eft ideals in Φ(''A'') from the structure theory of ideals for von Neumann algebras, which is relatively much more simple. If ''K'' is a norm-closed left ideal ...

...ch itself is a special case of various abstract Tauberian theorems about [[Banach algebra]]s. ...

...[[John von Neumann]]'s study of symmetric norms on [[linear algebra|matrix algebras]].<ref name="vN1">{{cite journal ...e Calkin correspondence, since the sequence space ''j'' is equivalent as a Banach space to the operators in the operator ideal ''J'' that are diagonal with r ...

...algebra]]s theory and [[operator algebra]]s, [[descriptive set theory]], [[Banach space]] theory, and [[quantum information]]."<ref>{{cite web|title=A tribut ...University]] in 1962. His thesis ''On Representations of <math>C^*</math>-algebras'' was supervised by [[George Mackey]].<ref name=MathGen>{{MathGenealogy|id= ...