تحت إشراف قسم الرياضيات والإحصاء وبالتعاون مع مركز البحوث بالكلية أقيم اليوم الثلاثاء 25/ 2/ 2020 سيمنار بعنوان :

" Toeplitz and Hankel Operators, Berezin Symbols, Englis Algebra and Properties"

قدمته  د. أماني باعظيم وذلك في تمام الساعة ٩:٠٠ ص في قاعة الاجتماعات بكلية العلوم.

ملخص البحث :

 We study how the properties of an operator are reected in the properties of its Berezin symbol and membership to Engli algebras. The rst chapter of the thesis is an introduction, where we discuss the history of the subject. Then, we give some necessary facts about the Hardy Hilbert space over the unit disc D, also we collected some necessary facts from functional analysis. We collected main denitions and facts about Hankel and Toeplitz operators, Berezin symbols of operators and Englialgebras. We consider Berezin symbols and Hankel operators on the Hardy space over the unit disc D and give their applications. Namely, we estimate in term of Hankel operators and Berezin symbols, the distances from a given operator to the algebra of all analytic Toeplitz operators and to the set of all Toeplitz operators on H2: We also consider the model operator M on the model space K. We use Hankel operators also to prove some lower estimate for the so called Berezin number of bounded linear operator, we consider the Berezin -sequence, where is an operator valued inner function, for operators on the vector valued Hardy , and study the invertibility of some operators in the model space via the Berezin -sequence. By applying Berezin symbols technique and Engli algebra, the Toeplitz Corona Problem in the Bergman space a of analytic functions on D is studied. Moreover, C-invertibility and C-unitarity of operators are also introduced and studied.

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