11 papers · 1 filter
Multipliers of uniform topological algebras
M. El Azhari
Let be a complete uniform topological algebra with Arens-Michael normed factors Then within an…
A non-unital algebra has UUNP iff its unitization has UUNP
M. El Azhari
Let be a non-unital Banach algebra, S. J. Bhatt and H. V. Dedania showed that has the unique uniform norm property (UUNP) if and only if its unitization has UUNP. Here we p…
On the paper: Numerical radius preserving linear maps on Banach algebras
M. El Azhari
We give an example of a unital commutative complex Banach algebra having a normalized state which is not a spectral state and admitting an extreme normalized state which is not mul…
Functional continuity of unital -algebras with orthogonal bases
M. El Azhari
Let be a unital -algebra with an orthogonal basis, then every multiplicative linear functional on is continuous. This gives an answer to a problem posed by Z. Sawon…
Travaux de Husain et al. sur la continuité automatique des caractères
M. El Azhari
We give a survey of Husain, Ng and Liang's results concerning the automatic continuity of algebra homomorphisms. We also give the improvements obtained by Joseph, Akkar, Oudadess,…
Positive linear functionals on BP*-algebras
M. El Azhari
Let A be a BP*-algebra with identity e, P_{1}(A) be the set of all positive linear functionals f on A such that f(e) = 1, and let M_{s}(A) be the set of all nonzero hermitian multi…
A real seminorm with square property is submultiplicative
M. El Azhari
A seminorm with square property on a real associative algebra is submultiplicative
On uniform topological algebras
M. El Azhari
The uniform norm on a uniform normed Q-algebra is the only uniform Q-algebra norm on it. The uniform norm on a regular uniform normed Q-algebra with unit is the only uniform norm o…
A real p-homogeneous seminorm with square property is submultiplicative
M. El Azhari
We give a functional representation theorem for a class of real p-Banach algebras. This theorem is used to show that every p-homogeneous seminorm with square property on a real ass…
On saturated uniformly A-convex algebras
M. El Azhari
Following ideas of A.C.Cochran, we give a suitable definition of a saturated uniformly A-convex algebra. In the m-convex case, such algebra is a uniform topological one.
A remark on continuity of positive linear functionals on separable Banach *-algebras
M. El Azhari
Using a variation of the Murphy-Varopoulos Theorem, we give a new proof of the following R.J.Loy Theorem: Let A be a separable Banach*-algebra with center Z such that ZA has at mos…