Functional Analysis, Operator Theory, Complex Analysis

We  discuss  the  distribution  of  spectra  of  a  direct  sum  decomposition  of  an
arbitrary operator into normal and completely non normal parts. We utilize the fact that any
given operator  𝑇 ∈ 𝐵(𝐻) can be decomposed into a direct summand 𝑇 = 𝑇
1 ⊕ 𝑇
2
with 𝑇
1
and  𝑇
2
are  the  normal  and  completely  non  normal  parts  respectively.  This  canonical
decomposition  is  preferred  to  other  forms  of  decomposition  such  as  Polar  and  Cartesian
decompositions because these two do not transfer certain properties (for instance the spectra,
numerical  range,  and  numerical  radius)  from  the  original  /decomposed  operator  to  the
constituent parts. This is presumably done since these parts are simpler to deal with.

In this paper we introduce the quantum white noise (QWN) conservation operator N Q acting on nuclear algebra of white noise operators L(F θ (S ′ C (R)), F * θ (S ′ C (R))) endowed with the Wick product. Similarly to the classical case, we give a useful integral representation in terms of the QWNderivatives {D − t , D + t ; t ∈ R} for the QWN-conservation operator from which it follows that the QWN-conservation operator is a Wick derivation. Via this property, a relation with the Cauchy problem associated to the QWN-conservation operator and the Wick differential equation is worked out.

In this paper we introduce and prove some new concepts and results on
c-frames for Hilbert spaces. We define c-Riesz bases for a Hilbert space H and
state some results to characterize them. Then, we give necessary and sufficient
conditions on c-Bessel mappings f and g and operators L1;L2 on H so that L1f+
L2g is a c-frame for H. This allows us to construct a large number of new c-
frames by existing c-frames. Also, we define orthonormal mappings for H and
we specify a necessary and sufficient condition to represent a c-frame as a linear
combination of two orthonormal mappings. Moreover, we show that every c-frame
can be written as a (multiple of a) sum of two Parseval c-frames; it can also be
written as a (multiple of a) sum of an orthonormal mapping and a c-Riesz basis.

Sequencing projects arising from high-throughput technologies including those of sequencing DNA microarray allowed measuring simultaneously the expression levels of millions of genes of a biological sample as well as to annotate and to identify the role (function) of those genes. Consequently, to better manage and organize this significant amount of information, bioinformatics approaches have been developed. These approaches provide a representation and a more 'relevant' integration of data in order to test and validate the researchers' hypothesis. In this context, this article describes and discusses some techniques used for the functional analysis of gene expression data.

In this paper, we consider a new subclass of analytic and bi-univalent functions associated with q-Ruscheweyh differential operator in the open unit disk U. For functions belonging to the class Σ q (λ, φ), we obtain estimates on the first two Taylor-Maclaurin coefficients. Further, we derive another subclass of analytic and bi-univalent functions as a special consequences of the results.

A Poland philosopher, in 1920s, introduced the concept of three-valued logic which was later generalized to four-valued logic and finally to infinite-valued logic. This infinite-valued logic was the idea behind the concept of graded membership initiated by Zadeh (1965) which further gave birth to fuzzy logic. Nowadays, this concept of fuzziness is a popular field of research due to its application oriented significance.The aim of the present paper is to give a very brief overview of this development-from philosophical thought to theabstract theorems.

Abstract
Quality in higher education is the major concern among researchers. Managing quality in higher education in a
multicultural population with different approaches is not only challenging but an uphill task. This paper will
focus on quality concern in higher education keeping in view, the United Arab Emirates (UAE) perspectives. A
model to maintain the quality in higher education and current higher education quality practices in UAE will be
explored along with its challenges.
Keywords: quality, higher education, UAE perspective

demostró muchos resultados importantes en elárea de espacios localmente convexos. Para estudiar algunos de sus resultados, primero veremos algunos conceptos del cálculo en el contexto de dos variables. Después veremos que estos conceptos se generalizan a espacios normados. Un concepto básico es el de continuidad:

As a further generalization of paranormal operators, we shall introduce a new class " absolute-(p, r)-paranormal " operators for p > 0 and r > 0 such that |T | p |T * | r x r ≥ ≥|T * | r x p+r for every unit vector x. And we shall show several properties on absolute-(p, r)-paranormal operators as generalizations of the results on absolute-k-paranormal and p-paranormal operators introduced in [10] and [6], respectively.

We admitted following : If ,, a ,, real numbers and i=sqr(-1) , a->+inf ai->complex infinity (Cinf) ,if a->-inf ai->complex infinity ! With other terms (+/-infinity) is include in Complex (absolute) infinity ! We easy to observe Riemann zeta function z=Produce(p prime numbers)1/[1-p^-(1/2+ai) ] have zero`s valuable for initial condition true P(1) ,and uses P(n)->P(n+1) is an results of Hardy-Lovasz Peter conjecture,but why z(1/2+ai)=0 (for a negative integer is true) ? We introduced Complex Infinity z= 1/(1-inf complex)=1/Complexinfinity=0 ! (author p lovasz 4 27 2021 ,Huedin Romania,all right reserve) !

In this work we study the essential spectra of composition operators
on weighted Bergman spaces of analytic functions which might be termed
as “quasi-parabolic.” This is the class of composition operators on A2
 with
symbols whose conjugate with the Cayley transform on the upper half-plane
are of the form ϕ(z) = z + ψ(z), where ψ ∈ H1(H) and ℑ(ψ(z)) > ǫ > 0.
We especially examine the case where ψ is discontinuous at infinity. A new
method is devised to show that this type of composition operators fall in a C*-
algebra of Toeplitz operators and Fourier multipliers. This method enables us
to provide new examples of essentially normal composition operators and to
calculate their essential spectra.

We look for characterizations of those locally convex spaces that satisfy the strict Mackey convergence condition within the context of spaces with webs. We will say that a locally convex space has a boundedly compatible web if it has a web of absolutely convex sets whose members behave like zero neighborhoods in a metrizable locally convex space. It will be shown that these locally convex spaces satisfy the strict Mackey convergence condition. One consequence of this result will be a characterization of boundedly retractive inductive limits. We will also prove that if E is locally complete and webbed, then the strict Mackey convergence condition is equivalent to E having a boundedly compatible web.