Serdica Mathematical Journal
Volume 45, Number 1, 2019
C O N T E N T S
·
Shchukin, M.
On 2-homogeneous C*-algebras over two-dimensional oriented manifolds generated by three idempotents
(pp. 1−8)
·
Sharma, C., K. Raj.
Generalized strong Cesàro spaces of lacunary statistical convergent sequences
(pp. 9−22)
·
Sarić, B.
On Cauchy's residue theorem in ℝN
(pp. 23−34)
·
Sharma, R. K., A. B. Singh
Zip property of skew Hurwitz series rings and modules
(pp. 35−54)
·
Ellouz, H., I. Feki, A. Jeribi.
On the asymptotic behavior of the eigenvalues of an analytic operator
in the sense of Kato and applications
(pp. 55−88)
A B S T R A C T S
ON 2-HOMOGENEOUS C*-ALGEBRAS OVER TWO-DIMENSIONAL ORIENTED MANIFOLDS GENERATED BY THREE IDEMPOTENTS
Mikhail Shchukin
mvs777777@gmail.com
2010 Mathematics Subject Classification:
Primary 46L05, Secondary 16U99.
Key words:
n-homogeneous C*-algebras, idempotent, two-dimensional manifold, number of generators, operator algebras.
We consider algebraic bundles over a two-dimensional compact oriented connected manifold. In 1961 J. Fell, J. Tomiyama, M. Takesaki showed that every n-homogeneous C*-algebra is isomorphic to the algebra of all continuous sections for the appropriate algebraic bundle. By using this realization we prove in the work that every 2-homogeneous C*-algebra over two-dimensional compact oriented connected manifold can be generated by three idempotents. Such algebra can not be generated by two idempotents.
GENERALIZED STRONG CESÀRO SPACES OF LACUNARY STATISTICAL CONVERGENT SEQUENCES
Charu Sharma
charu145.cs@gmail.com,
Kuldip Raj
kuldipraj68@gmail.com
2010 Mathematics Subject Classification:
40A35, 40C05, 46A45.
Key words:
modulus function, lacunary sequence, Generalized difference sequence space, density, statistical convergence, strong Cesàro summability.
In this paper, we introduce and study the concepts of f-lacunary statistical convergence of order α and strong Cesàro summability of order α with respect to modulus function f and lacunary sequence &theta = (kr). Further, using these concepts we define some sequence spaces Sα(f, θ, Δmv, u) of all f-lacunary statistical convergence of order α and wα(f, θ, Δmv, u) of all strong Cesàro summability of order α. We also investigate some inclusion relations between these spaces.
ON CAUCHY'S RESIDUE THEOREM IN ℝN
Branko Sarić
saric.b@mts.rs
2010 Mathematics Subject Classification:
Primary 26B20; Secondary 26A39.
Key words:
Spatial (integral) derivative, total HN̂ integrability,
Cauchy's residue theorem.
A method of spatial (integral) differentiation of multivector fields in a k-dimensional hyper-rectangle [a, b] immersed in ℝN has been introduced. For a class of discontinuous multivector fields a new concept of a residual field as well as the concept of total 𝒦ℋ-integrability have been defined. Finally, this has led naturally to an extension of Cauchy's residue theorem in ℝN.
ZIP PROPERTY OF SKEW HURWITZ SERIES RINGS AND MODULES
R. K. Sharma
rksharmaiitd@gmail.com,
Amit B. Singh
amit.bhooshan84@gmail.com
2010 Mathematics Subject Classification:
16S85, 16U80, 16S10.
Key words:
zip ring, zip module, Σ-zip ring, skew Hurwitz series ring, skew Hurwitz series module, reduced ring, ω-compatible ring, ω-compatible module, skew Hurwitz series-wise Armendariz, ω-Armendariz of skew Hurwitz series type.
Carl Faith [Rings with zero intersection property on annihilators: ZIP rings.
Publ. Math. 33, No 2 (1989), 329−332] called a ring R to be right zip if the right annihilator rR(X) of a subset
X of R is zero, then there exists a finite subset Y ⊆ X such that rR(Y) = 0; equivalently, for a left ideal L of R with rR(L) = 0, there exists a finitely generated left ideal L1 ⊆ L such that rR(L1) = 0. In this article, we study the behavior of zip property of the skew Hurwitz series rings and modules for the non-commutative ring. In particular, we prove the following results:
(1) Let R be a ring and ω be an endomorphism of R. If R is skew Hurwitz series-wise Armendariz and ω-compatible, then R is a right zip ring if and only if the skew Hurwitz series ring (HR, ω) is a right zip ring.
(2) Let MR be a module and ω be an endomorphism of R. If MR is ω-Armendariz of skew Hurwitz series type and ω-compatible, then MR is a zip right R-module if and only if the skew Hurwitz power series module HM(HR, ω) is a zip right (HR, ω)-module.
(3) Let R be a ring, I a Σ-compatible semi prime ideal of R and\break char(R/I) = 0, then R is a &SigmaI-zip ring if and only if the skew Hurwitz power series ring (HR, ω) is a Σ(HI, ω)-zip ring.
ON THE ASYMPTOTIC BEHAVIOR OF THE EIGENVALUES OF AN ANALYTIC
OPERATOR IN THE SENSE OF KATO AND APPLICATIONS
Hanen Ellouz
ellouze.hanen@hotmail.fr,
Ines Feki
feki.ines@yahoo.fr,
Aref Jeribi
Aref.Jeribi@fss.rnu.tn
2010 Mathematics Subject Classification:
47A55, 15A42, 65H17, 47B25.
Key words:
elastic membrane, Gribov operator, not condense, self-adjoint, spectrum.
In the present paper, we derive a precise description to the behavior of the spectrum of a self-adjoint operator T0 on a separable Hilbert space ℋ after a perturbation by an analytic operator
B(ε):= ε T1 +ε2T2+⋯+εk Tk+⋯,
where $ε ∈ ℂ and T1, T2, ... are linear operators on ℋ having the same domain 𝒟 ⊃ 𝒟(T0) and satisfying a specific growing inequality; while the spectrum of T0 is discrete and its eigenvalues are not condense. Moreover, we apply the obtained results to a Gribov operator in Bargmann space and to a problem of radiation of a vibrating structure in a light fluid.
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