In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...

Completely continuous operators Let A be a Banach algebra with |A| % {1}, where A := {a ∈ A : |ab| = |a| |b| for all b ∈ A} is the set of all multiplicative units in A (equivalently, A = {a ∈ A : |a| |a| = 1}). Then for any Banach modules M,N over A, an A-linear map L : M → N is continuous iff supm6=0 |L(m)| |m| < ∞. Let BA(M,N) be the space of such maps. With the norm |L| := supm6=0 |L(m)| |m|...

In this paper, we establish some new critical fixed point theorems for the sum $AB+C$ in a Banach algebra relative to the weak topology, where $frac{I-C}{A}$ allows to be noninvertible. In addition, a special class of Banach algebras will be considered.

–a notion of amenability for topological semigroups is introduced. a topological semigroup s iscalled johnson amenable if for every banach s -bimodule e , every bounded crossed homomorphism froms to e* is principal. in this paper it is shown that a discrete semigroup s is johnson amenable if and only if1(s) is an amenable banach algebra. also, we show that if a topological semigroup s is johns...

let  be a banach algebra. let  be linear mappings on . first we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple banach algebras, in certain case. afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

Assuming the generalized continuum hypothesis we construct arbitrarily big indecomposable Banach spaces. i.e., such that whenever they are decomposed as X ⊕ Y , then one of the closed subspaces X or Y must be finite dimensional. It requires alternative techniques compared to those which were initiated by Gowers and Maurey or Argyros with the coauthors. This is because hereditarily indecomposabl...

For each triple of positive numbers p,q,r ≥ 1 and each commutative C-algebra with identity 1 and the set s( ) of states on , the set r ( ) of all matrices A = [ajk] over such that φ[A [r] ] := [φ(|ajk|r )] defines a bounded operator from p to q for all φ ∈ s( ) is shown to be a Banach algebra under the Schur product operation, and the norm ||A|| = |||A|||p,q,r = sup{||φ[A[r] ]||1/r : φ ∈ s( )}....

The paper continues the study of differential Banach *algebras AS and FS of operators associated with symmetric operators S on Hilbert spaces H. The algebra AS is the domain of the largest *-derivation δS of B(H) implemented by S and the algebra FS is the closure of the set of all finite rank operators in AS with respect to the norm ‖A‖ = ‖A‖+‖δS(A)‖. When S is selfadjoint, FS is the domain of ...

Unless we say otherwise, every vector space we talk about is taken to be over C. A Banach algebra is a Banach space A that is also an algebra satisfying ‖AB‖ ≤ ‖A‖ ‖B‖ for A,B ∈ A. We say that A is unital if there is a nonzero element I ∈ A such that AI = A and IA = A for all A ∈ A, called a identity element. If X is a Banach space, let B(X) denote the set of bounded linear operators X → X, and...