A non-zero lower semi-continuous semi-finite trace $ f $
on a [[C*-algebra| $ C ^ {*} $-
2 KB (358 words) - 14:43, 27 January 2024
...t operators (cf. [[Hilbert–Schmidt operator|Hilbert–Schmidt operator]]) on a given Hilbert space.
...Neumann algebras and traces on them; a certain extension of the concept of a Hilbert algebra makes it possible to study by similar means von Neumann alg
3 KB (457 words) - 18:32, 28 June 2015
$#A+1 = 33 n = 0
$#C+1 = 33 : ~/encyclopedia/old_files/data/H047/H.0407350 Hilbert\ANDSchmidt op
3 KB (501 words) - 22:10, 5 June 2020
'' $ A $''
on the set $ A ^ {+} $
3 KB (490 words) - 13:58, 21 January 2024
$#A+1 = 33 n = 0
$#C+1 = 33 : ~/encyclopedia/old_files/data/L057/L.0507990 Lefschetz number
3 KB (494 words) - 08:31, 6 January 2024
$#A+1 = 36 n = 1
$#C+1 = 36 : ~/encyclopedia/old_files/data/C021/C.0201580 Character of a representation of an associative algebra
3 KB (388 words) - 09:31, 26 March 2023
...eory|$K$-theory]] index of an invariant (pseudo-) differential operator on a covering $\tilde { M } \rightarrow M$ with [[Galois group|Galois group]] (o
The ingredients of this theorem are stated in more detail below. Let $M$ be a smooth compact [[Manifold|manifold]].
5 KB (698 words) - 17:02, 1 July 2020
$#A+1 = 15 n = 0
$#C+1 = 15 : ~/encyclopedia/old_files/data/M063/M.0603440 Mercer theorem
3 KB (405 words) - 08:00, 6 June 2020
$#A+1 = 239 n = 2
$#C+1 = 239 : ~/encyclopedia/old_files/data/N067/N.0607850 Nuclear operator,
24 KB (3,574 words) - 18:23, 21 January 2021
...mi-normal operators is one of the few well-developed spectral theories for a class of non-self-adjoint operators. For the latter, see [[#References|[a3]
...mi-normal operators are obtained via the Berger–Shaw inequality: If $T$ is a hyponormal operator (i.e. $[T^*,T]\geq 0$), of finite rational cyclicity $r
6 KB (970 words) - 07:33, 18 March 2023
...norm permitting composition that is not alternative. For more information on these algebras, their generalizations and the physics, see [[#References|[a
...ing $\widetilde { P _ { 8 } }$ of $P _ { 8 }$ under the product $*$ and is a division algebra over the real numbers. Both the algebras $P _ { 8 }$ and $
7 KB (944 words) - 10:21, 8 March 2021
...elong to the algebra $A$. A more frequently considered case is when $A$ is a [[Banach algebra|Banach algebra]] with respect to the norm
...alization of $C^*$-algebras (in particular, $C^*$-algebras with continuous trace) as algebras of vector functions are known. These theorems in turn permit o
2 KB (291 words) - 16:02, 10 July 2014
...(PI-rings). A ring $R$ is a PI-ring (cf. also [[PI-algebra]]) if there is a polynomial in the [[free associative algebra]] $\mathbf{Z}\langle x_1,x_2,\
...Amitsur–Levitzki theorem says that the ring of $(n\times n)$-matrices over a commutative ring satisfies the standard polynomial of degree $2n$, and no p
4 KB (628 words) - 21:20, 11 December 2017
...cci tensor|Ricci tensor]] components $R _ { a b } \equiv R _ { a c b } ^ { c }$, and the Ricci scalar $R=R_{ab}g^{ab}$ (and with square brackets denotin
...{ A B }$ where each capital index can take a value $1$–$6$ and represents a pair of skew indices according to the scheme:
6 KB (975 words) - 15:02, 30 March 2023
...examples of exotic phenomena. A (separable) [[C*-algebra|$C^*$-algebra]] $A$ is said to be an ''AF-algebra'' if one of the following two (not obviously
...ilon>0$ there exists a finite-dimensional sub-$C^*$-algebra $B$ of $A$ and a subset $\{b_1,\dots,b_n\}$ of $B$ with $\|a_j-b_j\|<\epsilon$ for all $j=1,
12 KB (1,766 words) - 06:39, 26 March 2023
...at detecting and classifying the nature of junctions in the image domain. A main reason why corner detection is important is that junctions provide imp
...under simple conditions, it relies on [[Edge detection|edge detection]] as a pre-processing stage and suffers from inherent limitations. For example, no
5 KB (686 words) - 16:45, 1 July 2020
A global Artin root number is a [[Complex number|complex number]] $W ( \rho )$ of modulus $1$ appearing in
in which $\rho$ is a representation
12 KB (1,811 words) - 17:46, 1 July 2020
$#A+1 = 221 n = 1
$#C+1 = 221 : ~/encyclopedia/old_files/data/U095/U.0905570 Unitary representati
24 KB (3,516 words) - 08:27, 6 June 2020
$#A+1 = 27 n = 0
$#C+1 = 27 : ~/encyclopedia/old_files/data/P075/P.0705780 Pseudo\AAhquadratic f
2 KB (328 words) - 13:15, 7 April 2023
$#A+1 = 29 n = 0
$#C+1 = 29 : ~/encyclopedia/old_files/data/A010/A.0100840 Adjoint linear transformation
2 KB (314 words) - 16:09, 1 April 2020