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## Studia Mathematica

1991 | 100 | 1 | 87-94
Tytuł artykułu

### Inequalities for exponentials in Banach algebras

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For commuting elements x, y of a unital Banach algebra ℬ it is clear that $∥e^{x+y}∥ ≤ ∥e^x∥ ∥e^y∥$. On the order hand, M. Taylor has shown that this inequality remains valid for a self-adjoint operator x and a skew-adjoint operator y, without the assumption that they commute. In this paper we obtain similar inequalities under conditions that lie between these extremes. The inequalities are used to deduce growth estimates of the form $∥e'^{<x,ξ>}∥ ≤ c(1 + |ξ|⟩^s$ for all $ξ ∈ R^m$, where $x = (x_1,..., x_m) ∈ ℬ^m$ and c, s are constants.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
87-94
Opis fizyczny
Daty
wydano
1991
otrzymano
1990-11-12
Twórcy
autor
• Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia
Bibliografia
• [1] A. McIntosh and A. Pryde, A functional calculus for several commuting operators, Indiana Univ. Math. J. 36 (1987), 421-439.
• [2] A. McIntosh, A. Pryde and W. Ricker, Estimates for solutions of the operator equation $∑^m_{j=1} A_j Q B_j = U$, in: Operator Theory: Adv. Appl. 28, Birkhäuser, Basel 1988, 43-65.
• [3] A. McIntosh, A. Pryde and W. Ricker, Systems of operator equations and perturbation of spectral subspaces of commuting operators, Michigan Math. J. 35 (1988), 43-65.
• [4] A. Pryde, A non-commutative joint spectral theory, Proc. Centre Math. Anal. Canberra 20 (1988), 153-161.
• [5] H. Radjavi, A trace condition equivalent to simultaneous triangularizability, Canad. J. Math. 38 (1986), 376-386.
• [6] M. Reed and B. Simon, Methods of Modern Mathematical Physic. I, II, Academic Press, New York 1980.
• [7] M. E. Taylor, Functions of several self-adjoint operators, Proc. Amer. Math. Soc. 19 (1968), 91-98.
• [8] C. Thompson, Inequalities and partial orders on matrix spaces, Indiana Univ. Math. J. 21 (1971), 469-480.
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Bibliografia
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