A C*-algebra is a complex Banach algebra together with an isometric antilinear involution satisfying (a b)* = b* a* and the C*-identity ‖a* a‖ = ‖a‖². Related tags: [tag:banach-algebras], [tag:von-neumann-algebras], [tag:operator-algebras], [tag:spectral-theory].

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### Hilbert space separability for spectral triples

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### Idempotents in Group Algebras

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### Approximation of unity by projectors

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### An example of a sequence of finite projections

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### Characterizing fullness of a von Neumann algebra by the topology of its bimodules

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### Does Borel functional calculus commute with *-isomorphism?

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### Closeness of points in the irreducible decomposition of a C$^{*}$-algebra representation

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### How rich the group of unitary elements in a von Neumann algebra to get “Murray-von Neumann” equivalence?

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### Schröder–Bernstein for representations of operator algebras

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### Extending maps from dense $*$-algebras of $C^*$-algebras

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### finite dimensional C*-algebras

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### is the conditional expectation faithful?

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### Generator of $K_0(C_0(\mathbb{C}))$

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### Non-existence of projections in crossed product

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### Pure infiniteness of tensor product $C^\ast$-algebras

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### A precise definition of contractible Banach algebras

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### Is the ideal property of $X^{**}$ inheritable to $X$?

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### Relation between maximal and reduced group $C^*$-algebras

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### Is every nontrivial idempotent in the Cuntz algebra, a commutator element?

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### Simple $C^*$ algebras whose all commutator elements have scalar square

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### Open projections and Murray-von Neumann equivalence

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### The groupoid $C^*$ algebra associated to a certain groupoid

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### Solvability of a certain functional equation in simple $C^*$ algebras

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### Regarding spectral radius

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### When is K0 of a C* algebra finitely generated?

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### The product of two controlled operators is also a controlled operator

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### C*-algebras: Existence of an element inducing an injective map

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### Full spectrum positive elements of a $C^*$-algebra

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### C*-algebra of a singular surface foliation

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### Homomorphism to multiplier algebra of groupoid $C^\ast$-algebra

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### an inverse semigroup (and perhaps a $C^*\!$-algebra) associated with a directed graph

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### Factor traces of the Temperley-Lieb algebra

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### Are algebraically isomorphic $C^*$-algebras $*$-isomorphic?

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### Finitely generated $K_0$ of $C^*$-algebras

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### A property of compact topological space via certain $C^*$ embedding in operator algebras

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### Modules of algebras with idempotents and the Stone-von Neumann theorem

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### Algebraic tensor product of C*-algebras extends via ideals? Application to restriction theorem?

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### An operator valued Egoroff's theorem

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### Enveloping $C^*$-algebra

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### Closed two-sided ideals in $C(X,M_n)$

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### Extension of Coburn's theorem on isometry and Toeplitz algebra

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### Extensions of sub-homogeneous $C^*$-algebras are subhomogeneous

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### Continuity under various topologies for positive linear functionals

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### Masas in SAW*-algebras

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### Dualizing the trivial action on a $C^*$-algebra

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### Non-invertible version of unitary intertwiners between correspondences of $C^\ast$-algebras

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### range of trace on projections: beyond rotation algebras

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### C*-algebra of free monogenic inverse semigroup

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### Characterizing (minimal) tensor product inside Hilbert C*-module

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