arXiv subjects
Publications and source records attributed to Pembe Ipek Al.
In this study, the classical results on the joint numerical radius for $n$-tuples of Hilbert space operators are extended to the setting of the joint $(f,δ)$-numerical radius. New and diverse contributions to this area are provided, including novel estimates for the lower and upper bounds of the $(f,δ)$-numerical radius in the context of sectorial operators.
In this article, in order to the minimal operator generated by the first-order differential-operator expression in the weighted Hilbert space of vector functions in the finite interval to be formal normal, the relationship between the variable operator coefficient of this differential-operator expression and the weight function is established. Afterwards, the general form of all normal extension of the minimal operator is found using the Glazman-Krein-Naimark Method. Then, the structure of spectrum of such extensions is investigated. Later on, the issue of belonging to Schatten von-Neumann classes is explored, as well as the asymptotic behaviour of the singular numbers of the inverse of such normal extensions. Lastly, an approach is developed on all normal extension expressed in the weighted Hilbert spaces.
In this paper, we present several new bounds for the norm and numerical radius of sums of Hilbert space operators. The obtained bounds form a new collection that enriches our understanding of these bounds. We compare our bounds with the existing literature using examples that demonstrate, in general, how our results are incomparable with the known bounds. Of particular interest are the treatment of the triangle inequality, the numerical radius of operator matrices, and singular value bounds for sums of operators.
In this study, some estimates are given for the $ (A,q)$-numerical radius and $ (A,q)$-Crawford number via the $ A$-numerical radius and $ A$-Crawford number for the $ A $-bounded linear operators in any complex semi-Hilbert space, respectively. Then, some evolutions are studied for the tensor product of two operators. Lastly, some convergence properties of the $ (A,q)$-numerical radius and $ (A,q)$-Crawford number, via the $ A$-uniform convergence of operator sequences, are investigated. We also considered several examples to illustrate our results. Finally, a few applications of some operator functions classes are also given.
In this article, firstly, some simple and smoothness properties of the weighted numerical radius and the weighted Crawford number functions are investigated. Then, some generalization formulas for lower and upper bounds of the weighted numerical radius function are obtained. Later on, some evaluations for lower and upper bounds of the weighted numerical index are given. The obtained results are generalized some well-known famous results about the special weighted numerical radius and the special weighted Crawford number functions in the recently literature. Also, the different and useful results are provided to the literature.