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European Mathematical Society Publishing House
2024-03-28 10:55:13
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PRIMS&vol=32&iss=3&update_since=2024-03-28
Publications of the Research Institute for Mathematical Sciences
Publ. Res. Inst. Math. Sci.
PRIMS
0034-5318
1663-4926
General
10.4171/PRIMS
http://www.ems-ph.org/doi/10.4171/PRIMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Research Institute for Mathematical Sciences, Kyoto University
32
1996
3
Cancellation and Non Cancellation Phenomena for Infinite Complexes
Yoshimi
Shitanda
Kyushu University, FUKUOKA, JAPAN
Let L(I, J) be defined by the pull-back of CP∞l → K(+Q, 2) ← Ω SJ3 where {I, J} is a partition of all primes. We classify spaces {Ωk Σk C(f)} of loop-suspension of mapping cone of phantom map f:L(l, J) → S3 for k = 0, 1, ⋯, ∞ which have the same n-type for all n. In the category of finite CW-complexes, cancellation and non cancellation phenomena are well studied. In the category of infinite CW-complexes, the phenomena are less known. We study cancellation and non cancellation phenomena for infinite dimensional complexes by using above spaces.
Algebraic topology
General
383
399
10.2977/prims/1195162848
http://www.ems-ph.org/doi/10.2977/prims/1195162848
Energy Decay and Asymptotic Behavior of Solutions to the Wave Equations with Linear Dissipation
Kiyoshi
Mochizuki
Chuo University, TOKYO, JAPAN
Hideo
Nakazawa
Tokyo Metropolitan University, TOKYO, JAPAN
Partial differential equations
General
401
414
10.2977/prims/1195162849
http://www.ems-ph.org/doi/10.2977/prims/1195162849
On the K-Theory of Cuntz-Krieger Algebras
David
Pask
University of Wollongong, WOLLONGONG, AUSTRALIA
Iain
Raeburn
University of Newcastle, NEWCASTLE, AUSTRALIA
We extend the uniqueness and simplicity results of Cuntz and Krieger to the countably infinite case, under a row-finite condition on the matrix A. Then we present a new approach to calculating the K-theory of the Cuntz-Krieger algebras, using the gauge action of T, which also works when A is a countably infinite 0-1 matrix. This calculation uses a dual Pimsner-Voiculescu six-term exact sequence for algebras carrying an action of T. Finally, we use these new results to calculate the K-theory of the Doplicher-Roberts algebras.
Functional analysis
General
415
443
10.2977/prims/1195162850
http://www.ems-ph.org/doi/10.2977/prims/1195162850
The Initial Value Problem for Cubic Semilinear Schrödinger Equations
Hiroyuki
Chihara
University of Tsukuba, TSUKUBA, JAPAN
We present local and global existence theorems for cubic semilinear Schrödinger equations. Our new results are the improvement of our previous ones ([2] , [3] , [4]). The idea of the proof consists of the energy and the decay estimates. These equations do not allow the classical energy estimates. To avoid this difficulty, we make strong use of S. Doi's method for linear Schrödinger type equations. Combining cubic nonlinearity and S. Doi's method, we obtain the improved results.
Partial differential equations
General
445
471
10.2977/prims/1195162851
http://www.ems-ph.org/doi/10.2977/prims/1195162851
On Localized Weak Precompactness in Banach Spaces
Minoru
Matsuda
Shizuoka University, SHIZUOKA, JAPAN
In this paper we make a study of K-weakly precompact sets A in Banach spaces. We give various characterizations of such sets by the effective use of the lifting theory, weak*-–A*-dentability and a K-valued weak*-measurable function constructed in the case where A is non-K-weakly precompact. These results also can be regarded as generalizations of corresponding ones on Pettis sets and weakly precompact sets.
Functional analysis
General
473
491
10.2977/prims/1195162852
http://www.ems-ph.org/doi/10.2977/prims/1195162852
An Application of Orthoisomorphisms to Non-Commutative Lp-Isometries
Keiichi
Watanabe
Niigata University, NIIGATA, JAPAN
We prove that if there exists an into linear isometry between non-commutative Lp-spaces then there exists an into Jordan * -isomorphism between underlying von Neumann algebras, as an application of Araki-Bunce-Wright's theorem concerning the characterization of orthogonality preserving positive maps between preduals. Moreover, we determine the structure of a linear non-commutative Lp-isometry when it is surjective and *-preserving.
Functional analysis
General
493
502
10.2977/prims/1195162853
http://www.ems-ph.org/doi/10.2977/prims/1195162853
Asymptotic Behavior of Blowup Solutions of a Parabolic Equation with the p-Laplacian
Ataru
Fujii
University of Tokyo, TOKYO, JAPAN
Masahito
Ohta
University of Tokyo, TOKYO, JAPAN
We consider the blowup problem for ut = Δpu + ∣ u ∣ p–2u (x ∈ Ω, t > 0) under the Dirichlet boundary condition and p > 2. We derive sufficient conditions on blowing up of solutions. In particular, it is shown that every non-negative and non-zero solution blows up in a finite time if the domain Ω is large enough. Moreover, we show that every blowup solution behaves asymptotically like a self-similar solution near the blowup time. The Rayleigh type quotient introduced in Lemma A plays an important role throughout this paper.
Partial differential equations
General
503
515
10.2977/prims/1195162854
http://www.ems-ph.org/doi/10.2977/prims/1195162854
Outer Automorphism Group of the Ergodic Equivalence Relation Generated by Translations of Dense Subgroup of Compact Group on its Homogeneous Space
Sergey
Gefter
Kharkov State University, KHARKOV, UKRAINE
We study the outer automorphism group OutRr of the ergodic equivalence relationRr generated by the action of a lattice Γ in a semisimple Lie group on the homogeneos space of a compact group K. It is shown that OutRr is locally compact. If K is a connected simple Lie group, we prove the compactness of 0utRr using the D. Witte's rigidity theorem. Moreover, an example of an equivalence relation without outer automorphisms is constructed.
Measure and integration
General
517
538
10.2977/prims/1195162855
http://www.ems-ph.org/doi/10.2977/prims/1195162855
The Essential Singularity of the Solution of a Ramified Characteristic Cauchy Problem
Hideshi
Yamane
University of Tokyo, TOKYO, JAPAN
Partial differential equations
General
539
554
10.2977/prims/1195162856
http://www.ems-ph.org/doi/10.2977/prims/1195162856