A multi-dimensional spectral theory in C*-algebras
A note on the differences of the consecutive powers of operators
We present two examples. One of an operator T such that 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 is convergent to zero but T is not power bounded.
A note on the joint spectrum in commutative Banach algebras
A note on the spectral mapping theorem
Addendum to "On product formulas for exponential functions".
Algebras whose groups of units are Lie groups
Let A be a locally convex, unital topological algebra whose group of units is open and such that inversion is continuous. Then inversion is analytic, and thus is an analytic Lie group. We show that if A is sequentially complete (or, more generally, Mackey complete), then 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 is an analytic Lie group without...
An axiomatic approach to joint spectra I
Applications of harmonic functional calculus in a quotient involutive Banach algebra. (Applications du calcul fonctionnel harmonique dans une algèbre de Banach involutive quotient.)
Caracterisations de certaines algèbres de Banach par le calcul fonctionnel
We show that the Banach algebras with continuous involution are the Banach algebras which admit a harmonic functional calculus, while we prove that the hermitian commutative Banach algebras are exactly the involutive commutative Banach algebras that admit a real analytic functional calculus.
Caracterisations des C*-algèbres par le calcul fonctionnel.
We prove that C*-algebras for an equivalent norm are the involutive Banach algebras which admit the continuous functional calculus.
Compatibilite du calcul fonctionnel holomorphe global avec les homomorphismes continus d΄ algebres de Banach
Concerning entire functions in -algebras
We construct a non-m-convex non-commutative -algebra on which all entire functions operate. Our example is also a Q-algebra and a radical algebra. It follows that some results true in the commutative case fail in general.
Continuity of the Drazin inverse II
We study the continuity of the generalized Drazin inverse for elements of Banach algebras and bounded linear operators on Banach spaces. This work extends the results obtained by the second author on the conventional Drazin inverse.
Division Formulas for Holomorphic Mappings with Values in Banach Algebra.
Elements of C*-algebras commuting with their Moore-Penrose inverse
We give new necessary and sufficient conditions for an element of a C*-algebra to commute with its Moore-Penrose inverse. We then study conditions which ensure that this property is preserved under multiplication. As a special case of our results we recover a recent theorem of Hartwig and Katz on EP matrices.
Embedding C(K) in B(X).
Exponential bounds for noncommuting systems of matrices
It is shown that a finite system T of matrices whose real linear combinations have real spectrum satisfies a bound of the form . The proof appeals to the monogenic functional calculus.
Extension d'un théorème de von Neumann dans les a*-algèbres.
Extension of Analytic Functional Calculus Mappings and Duality by ...-Closed Forms with Growth.
Finite-dimensional Lie subalgebras of algebras with continuous inversion
We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness condition. We find that these are precisely the linear Lie groups, that is, the Lie groups which can be faithfully represented as matrix groups. Our method relies on proving that certain finite-dimensional Lie subalgebras of algebras with continuous inversion commute...