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Volume 36, Issue 1
Displaying 1-5 of 5 articles from this issue
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Hiroshi Aso2000 Volume 36 Issue 1 Pages 1-18
Published: 2000
Released on J-STAGE: January 22, 2009
JOURNAL FREE ACCESSIt will be shown that any topological conjugacy of Z2-subshifts is factorized into a finite number of bipartite codes, and that in particular when textile shifts which are Z2-subshifts arising from textile systems introduced by Nasu are taken each bipartite code appearing in this factorization is given by a bipartite graph code of textile shifts which is defined in terms of textile systems. The latter result extends the Williams result on strong shift equivalence of Z1-topological Markov shifts to a Z2-shift case.View full abstractDownload PDF (1831K) -
Fabienne Prosmans2000 Volume 36 Issue 1 Pages 19-83
Published: 2000
Released on J-STAGE: April 24, 2009
JOURNAL FREE ACCESSIn this paper, we study the homological algebra of the category \mathcal{J}c of locally convex topological vector spaces from the point of view of derived categories. We start by showing that \mathcal{J}c is a quasi-abelian category in which products and direct sums are exact. This allows us to derive projective and inductive limit functors and to clarify their homological properties. In particular, we obtain strictness and acyclicity criteria. Next, we establish that the category formed by the separated objects of \mathcal{J}c is quasi-abelian and has the same derived category as \mathcal{J}c. Since complete objects of \mathcal{J}c do not form a quasi-abelian category, we are lead to introduce the notion of cohomological completeness and to study the derived completion functor. Our main result in this context is an equivalence between the subcategory of D(\mathcal{J}c) formed by cohomologically complete complexes and the derived category of the category of pro-Banach spaces. We show also that, under suitable assumptions, we can reduce the computation of Ext's in \mathcal{J}c to their computation in Ban by means of derived projective limits. We conclude the paper by studying derived duality functors.View full abstractDownload PDF (4672K) -
Nariya Kawazumi, Youichi Shibukawa2000 Volume 36 Issue 1 Pages 85-109
Published: 2000
Released on J-STAGE: April 24, 2009
JOURNAL FREE ACCESSWe give all the meromorphic functions defined near the origin 0∈\mathbb{C} satisfying a functional equation investigated by Bruschi and Calogero [1], [2].View full abstractDownload PDF (2008K) -
Hiroshi Yamada2000 Volume 36 Issue 1 Pages 111-138
Published: 2000
Released on J-STAGE: January 22, 2009
JOURNAL FREE ACCESSDownload PDF (2021K) -
Gert K. Pedersen2000 Volume 36 Issue 1 Pages 139-157
Published: 2000
Released on J-STAGE: April 24, 2009
JOURNAL FREE ACCESSWe study the Banach *-algebra Cop1(I) of C1-functions f on the compact interval I such that the corresponding Hilbert space operator function T→f(T), for T=T* and sp(T)⊂I, is Fréchet differentiable. If f(x)=∫eitx\widehat{f}(t)dt we know that the differential is given by the formula
dfT(S)=∫−∞∞∫01UstSU(1−s)tds\widehat{f'} (t)dt,
where Ut=exp(itT). Functions of this type are dense in Cop1(I), and C2(I)⊂Cop1(I)⊂C1(I), so several classical results can be deduced. In particular we show that if T∈\mathfrak{D}(δ), where δ is the generator of a one-parameter group of *-automorphisms of a C*-algebra \mathfrak{A} (or just a closed *-derivation in \mathfrak{A}), then f(T)∈\mathfrak{D}(δ) for every f in Cop1(I), where sp(T)⊂I, and
δ(f(T))=dfT(δ(T)).View full abstractDownload PDF (1748K)
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