Inequalities for exponentials in Banach algebras

• Autorzy: A. J. Pryde
• 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.

Kategorie tematyczne

• 47A30: Norms (inequalities, more than one norm, etc.)
• 15A45: Miscellaneous inequalities involving matrices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1991
• Tom: 100
• Numer: 1
• Strony: 87-94

Daty

wydano

1991

otrzymano

1990-11-12

Twórcy

autor

A. J. Pryde

• Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia

Bibliografia

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• [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.