...A more frequently considered case is when $A$ is a [[Banach algebra|Banach algebra]] with respect to the norm
$$\Vert x\Vert=\sup_{t\in T}\Vert x(t)\Vert_A(t),$$
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...e local nature of properties, see [[Mal'tsev local theorems|Mal'tsev local theorems]].
...that residually has the property $P$ actually has the property $P$ itself. In the class of all groups the property of being Abelian is residual, but fini
3 KB (536 words) - 22:24, 26 October 2014
...cyclopedia/old_files/data/F040/F.0400240 Finite\AAhdimensional associative algebra
An associative algebra (cf. [[Associative rings and algebras|Associative rings and algebras]]) $
4 KB (607 words) - 20:54, 15 March 2023
...the mapping thus obtained form the essence of various duality theorems in algebra, topology and functional analysis.
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''of a [[Boolean algebra]] $\mathcal{B}$''
...Every totally-disconnected compact space is the Stone space of the Boolean algebra of its open-and-closed sets.
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...operator algebras in which one studies automorphisms of [[C*-algebra|$C^*$-algebra]]s from the point of view of [[ergodic theory]].
The range of questions considered in non-commutative ergodic theory and the results obtained so far (1984) can b
3 KB (481 words) - 21:35, 15 December 2014
...nd the [[linear span]] of $\operatorname { log } | A ^ { - 1 } |$ is dense in $\operatorname { Re } C ( X )$, where $A ^ { - 1 }$ is the family of invert
...of functions of a complex variable]]). Then $R ( X )$ is a hypo-Dirichlet algebra [[#References|[a3]]].
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...the algebra of Bohr almost-periodic functions (cf. [[Banach algebra|Banach algebra]]; [[Bohr almost-periodic functions|Bohr almost-periodic functions]]). The
algebra $ A $
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Theorems on the classical problems in the theory of functions of several complex variables, first proved by K. Ok
...in of holomorphy]] in $\mathbf C^n$; the second Cousin problem is solvable in any domain of holomorphy $D\subset\mathbf C^n$ that is homeomorphic to $D_1
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\left ( \wedge _ {i \in I } a _ {i} \right ) \
\wedge \left ( \lor _ {i \in I } b _ {i} \right ) = \
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...the semantics is defined by a [[Sigma-algebra (Computer Science)|$\Sigma$-algebra $A$]]. An interpretation $v^\ast \colon T(\Sigma,X) \longrightarrow A$ alwa
...nd terms $t\in T(\Sigma)$, i.e. terms which do not contain any variable $x\in X$, have an interpretation independent from $v$.
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algebra of Borel sets on the line, let $ \mathfrak F $
algebra of $ {\mathcal A} $,
2 KB (296 words) - 17:46, 4 June 2020
...gebraic variety or scheme. The structure sheaf of a Noetherian scheme and, in particular, of an algebraic variety is coherent.
...— analytic, formal, étale; and g) a theory of [[local cohomology]], useful in the study of coherent algebraic sheaves on incomplete varieties. One of the
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...variable $\phi(\tau)$ whose behaviour, as a rule, is assumed to be known. In general, $\tau$ is a parameter that is a numerical characteristic of the ap
...direct and inverse theorems|Approximation of functions, direct and inverse theorems]]).
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...vanish on the group of characters $\hat G$ of $G$ and if $y$ is a function in $L^\infty(G)$ such that the convolution $(x*y)$ tends to zero at infinity o
...ve locally compact group, and on the possibility of [[spectral synthesis]] in group algebras for closed ideals belonging to only a finite number of regul
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of a commutative Banach algebra $ A $
...ransform|Fourier transform]] (for more details see [[Banach algebra|Banach algebra]]). The Gel'fand transform was introduced by I.M. Gel'fand [[#References|[1
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...groups with operators (E. Noether, W. Krull), whence follow the analogous theorems for invariant and fully-invariant series.
...lements in a lattice. 4) Generalizations of the Schreier and Jordan–Hölder theorems have been obtained for normal categories (see [[#References|[8]]]).
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...ame { lim } _ { n \rightarrow \infty } \mu _ { n } ( E ) = \mu ( E )$, $E \in \Sigma$:
...vergence conditions are imposed on certain subfamilies of a given $\sigma$-algebra; those subfamilies need not be $\sigma$-algebras. The following definitions
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algebra $ \mathfrak B $
for any $ B \in \mathfrak B $.
4 KB (559 words) - 17:46, 4 June 2020
''Eymard algebra''
...à-Talamanca algebra]] for notations) is called the Fourier algebra of $G$. In fact,
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