...=L(X,X)$ with multiplication (composition) of operators becomes a [[Banach algebra]], since for the operator norm
where $I$ is the identity operator (the [[unit element]] of the algebra). Other equivalent norms on $L(x)$ subject to the same condition are also i
8 KB (1,284 words) - 21:49, 6 June 2016
...ogic. The observation that the closed right ideals of a [[C*-algebra|$C^*$-algebra]] form a quantale satisfying the conditions that each element is right-side
...ts of the spectrum $\text{Max} A$ are the closed right ideals of the $C^*$-algebra $A$ (cf. [[#References|[a2]]], [[#References|[a6]]]). By the existence of a
13 KB (2,065 words) - 18:59, 12 December 2023
denote the composition of morphisms
...gn="top">[a1]</TD> <TD valign="top"> H. Cartan, S. Eilenberg, "Homological algebra" , Princeton Univ. Press (1956)</TD></TR>
5 KB (668 words) - 10:06, 11 November 2023
the group ring of $ G $ (cf. also [[Group algebra|Group algebra]]; [[Cross product|Cross product]]) over the rational integers $ \mathbf
by composition of $ \psi _ {0} $
7 KB (1,035 words) - 05:58, 19 March 2022
forms an Abelian group with respect to the composition: $ ( \theta + \psi ) _ {X} = \theta _ {X} + \psi _ {X} $,
given by the composition
29 KB (4,197 words) - 09:49, 26 March 2023
....encyclopediaofmath.org/legacyimages/m/m110/m110160/m11016038.png" /> to a
composition of semi-algebraic functions, <img align="absmiddle" border="0" src="https:/
...="top"> A. Tarski, J.C.C. McKinsey, "A decision method for elementary
algebra and geometry" , Univ. California Press (1951)</TD></TR>
9 KB (1,282 words) - 17:26, 22 February 2013
...s of the second class are used most often in [[Universal algebra|universal algebra]], and in automatic theorem proving procedures.
...is an algebra of type $L$ and $t \in T$, then $\widetilde { t }$ denotes a composition of some of the functions and constants $\widetilde { f }$, which is coded b
9 KB (1,433 words) - 17:00, 1 July 2020
...ns contain the identity mappings and are closed with respect to successive composition (or product) of mappings. A category $ \mathfrak C $
the following partial composition (product) rule is given: The product of two morphisms $ \alpha : A \righ
43 KB (6,447 words) - 09:17, 26 March 2023
...nt weights and are denoted by $\Lambda ^ { + } ( n , r )$. One depicts the composition $\lambda$ into $n$ parts by its associated [[Young diagram|Young diagram]]
Let $\lambda$ be a composition of $r$. A $\lambda$-tableau $t$ is a Young diagram of shape $\lambda$, wher
33 KB (5,081 words) - 10:26, 11 November 2023
...ves. This approach is strongly related to the first approach, as the Hecke algebra quadratic relation is analogous to the skein relation of the first method.
...and has a very nice reflection in the [[Jaeger composition product|Jaeger composition product]] [[#References|[a7]]].
18 KB (2,713 words) - 05:14, 15 February 2024
...and, more generally, to the open unit ball $U$ of a so-called $J ^ { * }$-algebra (see [[#References|[a37]]], [[#References|[a25]]] and the references there)
...gue of the Denjoy–Wolff theorem to the study of the eigenvalue problem for composition operators on Hardy spaces.
20 KB (3,130 words) - 07:34, 8 February 2024
.... Porta in their study [[#References|[a4]]] of linear $C_0$-semi-groups of composition operators on Hardy spaces. E. Vesentini investigated semi-groups of fractio
...et of all holomorphic vector fields on $\textbf{D}$ is a [[Lie algebra|Lie algebra]] under the commutator bracket
24 KB (3,989 words) - 20:19, 11 January 2021
...complex structure is defined by considering as $( 1,0 )$-forms on the Lie algebra of $\Omega G$, those with positive Fourier coefficients. Equivalently, $\Om
...n $M$ starting at a fixed basepoint. Here, the group operation is given by composition of loops. The space $LM$ has been considered in connection with the problem
5 KB (698 words) - 08:13, 15 February 2024
...pace#isomorphic|isomorphic]] to some compact metric space with the Borel σ-algebra;
...A)$ is isomorphic to some separable complete metric space with the Borel σ-algebra;
11 KB (1,769 words) - 05:54, 7 April 2018
$#C+1 = 1 : ~/encyclopedia/old_files/data/A011/A.0101340 Algebra
...ry, which marks the end of the "prehistory" of algebra. The development of algebra proper took place during the next three centuries, during which views as to
17 KB (2,478 words) - 16:09, 1 April 2020
which splits into the composition of a birational morphism
...'J. Soviet Math.'' , '''5''' : 6 (1976) pp. 803–864 ''Itogi Nauk. i Tekhn. Algebra Topol. Geom.'' , '''12''' (1974) pp. 77–170</TD></TR><TR><TD valign="top"
5 KB (749 words) - 07:33, 22 December 2023
...utomata and the feedback operation are chosen as $\Omega$ (cf. [[Automata, composition of]]). The criterion given above is applicable also in this case; it has be
...Kratko, "On the existence of non-recursive bases of finite automata" ''Algebra i Logika'' , '''3''' : 2 (1964) pp. 33–44 (In Russian)</TD></TR>
6 KB (920 words) - 20:06, 14 December 2016
...re multiplication of numbers, addition of vectors, successive performance (composition) of transformations, etc. The concept of a group is historically one of the
...an important role in the systematization and development of this branch of algebra.
21 KB (3,246 words) - 17:24, 9 October 2016
...aton is constructed, and the schemes of their composition (cf. [[Automata, composition of]]). Methods of specifying finite automata are described below.
may be specified as an algebra $ \langle S, \Phi \rangle $
25 KB (3,544 words) - 07:31, 26 March 2023
algebra $ A $
...Soviet Math.'' , '''7''' : 4 (1977) pp. 532–586 ''Itogi Nauk. i Tekhn. Algebra Topol. Geom.'' , '''13''' (1975) pp. 51–148</TD></TR><TR><TD valign="to
14 KB (2,048 words) - 09:29, 3 July 2021