Sentence examples for multiplication given by from inspiring English sources

These are double sequences of Hilbert spaces {X m,n }m,n="0∞ equipped with a multiplication given by coisometries from X i,j ⊗X k,l) to X(i+k,j+l).

In other words, the path algebra is linearly spanned by all paths in E, with the multiplication given by concatenation of paths (or zero if two paths cannot be concatenated).

The elements of M can be regarded as ordered pairs ( a, k ), where a ∈ A, k ∈ K with multiplication given by ( a, k ) ( a ′, k ′ ) = ( a a ′, ( k θ a ′ ) k ′ ).

The Heisenberg group H n is the set of points [ z, t ] ∈ C n × R with the multiplication given by [ z, t ] ⋅ [ z ′, t ′ ] = [ z + z ′, t + t ′ + 2 ℑ ( z ⋅ z ¯ ′ ) ], z, z ′ ∈ C n, t, t ′ ∈ R.

We prove that the set BrG(T) of Morita equivalence classes of such systems forms a group with multiplication given by the balanced tensor product: [A, α][B, β]=[A⊗C0(T) B, α⊗β], and we refer to BrG T) as the Equivariant Brauer Group.

Then the Schützenberger product of the monoids A and B, denoted by A ♢ B, is the set A × ℘ ( A × B ) × B (where ℘ denotes the power set) with the multiplication given by ( a 1, P 1, b 1 ) ( a 2, P 2, b 2 ) = ( a 1 a 2, P 1 b 2 ∪ a 1 P 2, b 1 b 2 ).

The multiplication is given by concatenating such symbols, imposing the distributive law under addition, and requiring that scalar multiplication commute with the tensor product ⊗, much the same way as with the tensor product of two vector spaces introduced above.

The result of the right multiplication is given by (17).

We characterize when T can be factorized through the space L2(m) by means of a multiplication operator given by a function of L2(∣∣m∣∣), where |m| is the variation of m, extending in this way the Maurey Rosenthal Theorem.

For (S, T in X), define (d:X times X rightarrow L(H)) by (d(T,S =pi_{|T-S|}), where (pi_{h}:HrighT,S =pi_{|T-S|}e multiplication operator given by (pi_{h}(phi)=hcdotphi) for (phiin H).

The sum of two such elements and is and scalar multiplication is given by.