RESULTS ON BANACH IDEALS AND SPACES OF MULTIPLIERS
... (cf. [23]). Thus Theorem 2.1 is applicable. If E is strongly character invariant, B is pseudosymmetric, because it is Banach module over F1 (G) with pointwise multiplication (cf. [11, Lemma 3.7 and 3.8]). Therefore Theorem 4.1 gives the result in this case. 1) 4.2 is not a special case of 4.1 becaus ...
... (cf. [23]). Thus Theorem 2.1 is applicable. If E is strongly character invariant, B is pseudosymmetric, because it is Banach module over F1 (G) with pointwise multiplication (cf. [11, Lemma 3.7 and 3.8]). Therefore Theorem 4.1 gives the result in this case. 1) 4.2 is not a special case of 4.1 becaus ...
of integers satisfying a linear recursion relation
... The restriction to the case of a difference equation of order 3 is mainly for convenience of notation and ease of illustration. The theorems in the first seven sections of the paper, which include my main result, may be immediately extended to the general case of a difference equation of order r. * ...
... The restriction to the case of a difference equation of order 3 is mainly for convenience of notation and ease of illustration. The theorems in the first seven sections of the paper, which include my main result, may be immediately extended to the general case of a difference equation of order r. * ...
J. Harding, Orthomodularity of decompositions in a categorical
... all projections are epic, and for each disjoint product diagram (f1 , f2 , f3 ) the diagram (f1 × f3 , f2 × f3 , π2 , π2 ) is a pushout. See Fig. 3. There are many examples of honest categories whose objects are based on sets and whose products are based on usual Cartesian products of sets; these in ...
... all projections are epic, and for each disjoint product diagram (f1 , f2 , f3 ) the diagram (f1 × f3 , f2 × f3 , π2 , π2 ) is a pushout. See Fig. 3. There are many examples of honest categories whose objects are based on sets and whose products are based on usual Cartesian products of sets; these in ...
Physical states on a
... linearity problem for physical states. The latter, in the form it is given above, is due to R. V. Kadison. I n w3 of the present paper we give a complete solution for the case of a physical state on a commutative C*-algebra A. When A is non-commutative, the problem remains unsolved in general. Howev ...
... linearity problem for physical states. The latter, in the form it is given above, is due to R. V. Kadison. I n w3 of the present paper we give a complete solution for the case of a physical state on a commutative C*-algebra A. When A is non-commutative, the problem remains unsolved in general. Howev ...
ON BOREL SETS BELONGING TO EVERY INVARIANT
... (2) C − C does not contain a neighbourhood of the neutral element of G, (3) C − C has empty interior. Leaving aside interrelations between κ-small and perfectly κ-small sets (see, however, Proposition 3.13), in the next two results we show that all Borel subsets of 2N with any of the properties unde ...
... (2) C − C does not contain a neighbourhood of the neutral element of G, (3) C − C has empty interior. Leaving aside interrelations between κ-small and perfectly κ-small sets (see, however, Proposition 3.13), in the next two results we show that all Borel subsets of 2N with any of the properties unde ...
as a PDF
... (b) It may happen that the net (fΦ /gΦ ) converges in L1 (Qg ) and its limit is not the Radon–Nikodym– density of Qf with respect to Qg . To obtain an example it is sufficient to consider a family (fα ) = (gα ) that generates two infinite products Qf and Qg (cf. (2.5)). (c) It may occasionally be t ...
... (b) It may happen that the net (fΦ /gΦ ) converges in L1 (Qg ) and its limit is not the Radon–Nikodym– density of Qf with respect to Qg . To obtain an example it is sufficient to consider a family (fα ) = (gα ) that generates two infinite products Qf and Qg (cf. (2.5)). (c) It may occasionally be t ...
HYPERELLIPTIC JACOBIANS AND SIMPLE GROUPS U3 1
... By Remark 3.2, the double transitivity implies that the F2 [U3 (q)]-module QB is absolutely simple. Since SU3 (Fq ) → U3 (q) is surjective, the corresponding F2 [SU3 (Fq )]-module QB is also absolutely simple. Recall that dimF2 (QB ) = #(B) − 1 = q 3 = 23m . By Theorem 4.3, there are no absolutely s ...
... By Remark 3.2, the double transitivity implies that the F2 [U3 (q)]-module QB is absolutely simple. Since SU3 (Fq ) → U3 (q) is surjective, the corresponding F2 [SU3 (Fq )]-module QB is also absolutely simple. Recall that dimF2 (QB ) = #(B) − 1 = q 3 = 23m . By Theorem 4.3, there are no absolutely s ...
Rationality of the quotient of P2 by finite group of automorphisms
... The plan of proof of Theorem 1.3 is the following. We want to find a normal subgroup N in G. If such a group exists then we consider the quotient P2k /N. Next, we G/N-equivariantly resolve the singularities of P2k /N, run the G/N-equivariant minimal model program [13] and get a surface X . Then we a ...
... The plan of proof of Theorem 1.3 is the following. We want to find a normal subgroup N in G. If such a group exists then we consider the quotient P2k /N. Next, we G/N-equivariantly resolve the singularities of P2k /N, run the G/N-equivariant minimal model program [13] and get a surface X . Then we a ...
on h1 of finite dimensional algebras
... We recall these well known results in the next section. We consider the case where I is a “pre-generated” ideal, the definition is given at section 3. This includes the cases I = 0 whenever Q has no oriented cycles, any ideal of a narrow quiver, and some other cases. An explicit dimension formula fo ...
... We recall these well known results in the next section. We consider the case where I is a “pre-generated” ideal, the definition is given at section 3. This includes the cases I = 0 whenever Q has no oriented cycles, any ideal of a narrow quiver, and some other cases. An explicit dimension formula fo ...
A co-analytic Cohen indestructible maximal cofinitary group
... this method seems open to a wider range of variation, allowing to construct mcgs with additional properties. An example of such a property is Cohenindestructibility, which we now define. For this, first observe that if G is a cofinitary group, then clearly it remains so in any extension of the unive ...
... this method seems open to a wider range of variation, allowing to construct mcgs with additional properties. An example of such a property is Cohenindestructibility, which we now define. For this, first observe that if G is a cofinitary group, then clearly it remains so in any extension of the unive ...
The Nil Hecke Ring and Cohomology of G/P for a Kac
... the minimal parabolic containing r;). Kac and Peterson have extended the definition of the ring of operators & on H(G/B) to the general case and they have used these operators to study the topology of G (as well as G/B). The problems, we wish to deal with, are to describe H(G/B): (I ) as a ring, in ...
... the minimal parabolic containing r;). Kac and Peterson have extended the definition of the ring of operators & on H(G/B) to the general case and they have used these operators to study the topology of G (as well as G/B). The problems, we wish to deal with, are to describe H(G/B): (I ) as a ring, in ...
Homomorphisms on normed algebras
... Theorem 2.3 cannot be applied since it is not known a priori that R is a Q-algebra in the norm \\T\\λ. If, however, the imbedding is discontinuous there exists a sequence {Tn} in R such that IITJIχ-^0 and ||5PJ|->oo. By the arguments of [1], the minimal ideals of R are the same as the minimal ideals ...
... Theorem 2.3 cannot be applied since it is not known a priori that R is a Q-algebra in the norm \\T\\λ. If, however, the imbedding is discontinuous there exists a sequence {Tn} in R such that IITJIχ-^0 and ||5PJ|->oo. By the arguments of [1], the minimal ideals of R are the same as the minimal ideals ...