Maps preserving semi-Fredholm operators on Hilbert C∗-modules

AbstractLet M be a Hilbert C∗-module over the C∗-algebra A, and LA(M) the C∗-algebra of all adjointable operators on M. Let φ:LA(M)→LA(M) be a unital linear map preserving semi-A-Fredholm operators in both directions and assume that φ is surjective up to compact operators. We will show that φ preserves compact operators and in certain cases, the induced map φ˜:LA(M)/KA(M)→LA(M)/KA(M) is an automorphism or an anti-automorphism

Generalized Induced Norms

Let ||.|| be a norm on the algebra M_n of all n-by-n matrices over the complex field C. An interesting problem in matrix theory is that "are there two norms ||.||_1 and ||.||_2 on C^n such that ||A||=max{||Ax||_2: ||x||_1=1} for all A in M_n. We will investigate this problem and its various aspects and will discuss under which conditions ||.||_1=||.||_2.Comment: 8 page

Surgical clipping compared to endovascular coiling of ruptured coil able middle cerebral aneurysms: A single-center experience

Objective: The middle cerebral artery (MCA) is the third most common site for ruptured intracranial aneurysms. Aneurysms in this location are known to be challenging to treat endovascularly and are commonly treated with microsurgery. Although advances in endovascular treatment options for cerebral aneurysms have markedly reduced the need for surgery in recent years and decades, there is no compelling scientific evidence that endovascular treatments are superior to surgical treatment. The present study aimed to determine the appropriate treatment modality in ruptured MCA aneurysms. Methods: We retrospectively evaluated and compared the treatment outcomes of 80 patients with ruptured MCA aneurysms who underwent either endovascular or microsurgical treatment in our center between 2011 and 2016. Post-treatment clinical and radiological outcomes were assessed in all patients. Furthermore, we compared intraoperative complications and the need for re-treatments between the two groups. Results: According to our findings, complete aneurysm occlusion was achieved in 90.5 and 89.2 of the patients in the clipping and coil group, respectively (p = 0.850). Moreover, 14.3 of the patients in the clipping group and 15.8 of the subjects in the coil group developed intraoperative complications (p = 0.851), including 3 cases of intraoperative hemorrhage and 3 cases of ischemia in the clipping group as well as 2 cases of thromboembolism and 4 cases of vasospasm during endovascular treatment in the coil group. There was an improvement in the modified Rankin score (mRS) at six months, with no significant difference between the two groups (p = 0.916). Conclusion: The results of coiling only with coil able MCA aneurysms were comparable to the results of clipping with difficult cases. Sufficient follow-up study of recurrence and retreatment are needed to determine the indication for coiling for ruptured MCA aneurysm. © 202

Derivations on Banach algebras

Let D be a derivation on a Banach algebra; by using the operator D2, we give necessary and sufficient conditions for the separating ideal of D to be nilpotent. We also introduce an ideal M(D) and apply it to find out more equivalent conditions for the continuity of D and for nilpotency of its separating ideal

Farthest Points and Subdifferential in -Normed Spaces

We study the farthest point mapping in a -normed space in virtue of subdifferential of ()=sup{‖−‖∶∈}, where is a weakly sequentially compact subset of . We show that the set of all points in which have farthest point in contains a dense subset of

Electronic Journal of Theoretical Physics Bi-parameter Semigroups of linear operators

Let X be a Banach space. We define the concept of a bi-parameter semigroup on X and its first and second generators. We also study bi-parameter semigroups on Banach algebras. A relation between uniformly continuous bi-parameter semigroups and σ-derivations is also established. It is proved that if {αt,s}t,s�0 is a uniformly continuous bi-parameter semigroup on a Banach algebra X, whose first and second generators are d and σ, respectively, and if d is also a σ-derivation then d n (ab) =(d + σ) n (a) ⋆ (d + σ) n (b) andαt,0(ab) =αt,1(a) ⋆αt,1(b) for all a, b ∈X