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A multi-dimensional spectral theory in C*-algebras

F. Vasilescu (1982)

Banach Center Publications

A note on the differences of the consecutive powers of operators

Andrzej Święch (1997)

Banach Center Publications

We present two examples. One of an operator T such that ${T^{n} (T - I)}_{n = 1}^{\infty}$ is precompact in the operator norm and the spectrum of T on the unit circle consists of an infinite number of points accumulating at 1, and the other of an operator T such that ${T^{n} (T - I)}_{n = 1}^{\infty}$ is convergent to zero but T is not power bounded.

A note on the joint spectrum in commutative Banach algebras

Vladimír Müller (1982)

Commentationes Mathematicae Universitatis Carolinae

A note on the spectral mapping theorem

Carlos Hernández-Garciadiego (1986)

Studia Mathematica

Addendum to "On product formulas for exponential functions".

S.Y. Shaw, C.Y. Lin (1986/1987)

Semigroup forum

Algebras whose groups of units are Lie groups

Helge Glöckner (2002)

Studia Mathematica

Let A be a locally convex, unital topological algebra whose group of units $A^{\times}$ is open and such that inversion $ι : A^{\times} \to A^{\times}$ is continuous. Then inversion is analytic, and thus $A^{\times}$ is an analytic Lie group. We show that if A is sequentially complete (or, more generally, Mackey complete), then $A^{\times}$ has a locally diffeomorphic exponential function and multiplication is given locally by the Baker-Campbell-Hausdorff series. In contrast, for suitable non-Mackey complete A, the unit group $A^{\times}$ is an analytic Lie group without...

An axiomatic approach to joint spectra I

W. Żelazko (1979)

Studia Mathematica

Applications of harmonic functional calculus in a quotient involutive Banach algebra. (Applications du calcul fonctionnel harmonique dans une algèbre de Banach involutive quotient.)

Akkar, M., Arroub, H. (1996)

Bulletin of the Belgian Mathematical Society - Simon Stevin

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