Showing papers in "Tohoku Mathematical Journal in 1959"

On the product projection of norm one in the direct product of operator algebras

Abstract: In the theory of operator algebras, the following result is known (cf. [2], [4], [9], [14]): If θι and θ2 are normal *-homomorphisms from W*-algebras Mj and M2 onto the other ΐ^*-algebras Nx and N2, then there exists the unique normal *-homomorphism θ from the T^*-direct product of M2 and M2, M j φ M s onto that of Nj and N2, N ^ N j such as 0θ(g) y) = θx(x) ® Θ2(y). Moreover, combining this result with that of Takeda [8], it can be shown that if θι and θ2 are *-homomorphisms from C*-algebras Mx and M2 onto the other C*-algebras Nj and N 2 there exists the unique *-homomorphism θ from the C*-direct product of Mx and M2, Mj ® M2, onto that of Nj and ® N2, 'Ni N 2 such as θ{x®y) — ^i( ̂ ) ® Θ2{y)' In both cases, if θ{ and θ2 are *-isomorphisms θ is a ^-isomorphism, too.

Arithmetic of group representations

Abstract: {M;k/o}={M1;o/o}+........+{M1; o/o}. If k=Q is the field of rationale and V is irreducible, this class number is always finite and was proved by C. Jordan [13]1. In the book of Speiser [20] this theorem was proved only in two special cases, namely, 3 is a cyclic group or V is absolutely irreducible. The reason for this may be explained by the following considerations. Let be a finite or infinite prime. We can consider P-extension M of the r-lattice M and put

Eine erweiterte asymptotische Darstellung der Lösung eines Systems von homogenen linearen Differentialgleichungen, welche von zwei Parametern abhängen

Abstract: Einleitung. In dieser Abhandlung mδchte ich die Abhandlung des Herrn Prof. Hukuhara erweitern. Andererseits erόrterte C. C. Hurd die asymptotische Entwicklung der Lδsung einer homogenen linearen Differentialgleichung n-ter Ordnung, welche von einem Parameter abhing. Ferner erorterte er die asymptotische Entwikklung der Lδsung einer homogenen linearen Differentialgleichung n-ter Ordnung, welche von zwei Parametern abhing. Dabei betrachtete er nur den Fall dass die charakteristische Gleichung verschiedene Wurzeln hatte. Es genϋgte ihm keine Voraussetzung zu betrachten, welche der charakteristischen Hilfsgleichung der Differentialgleichung entsprach, die auf einen Parameter abhίng. In meiner frύheren Abhandlung betrachtete ich die asymptotische Entwicklung der Lόsung eines Systems von homogenen linearen Difϊerentialgleichungen, welche auf zwei Parametern λ und μ abhingen :