Paper's Title:

Hyponormal and K-Quasi-Hyponormal Operators On Semi-Hilbertian Spaces

Author(s):

Ould Ahmed Mahmoud Sid Ahmed and Abdelkader Benali

Mathematics Department,
College of Science,
Aljouf University,
Aljouf 2014,
Saudi Arabia.
E-mail: sididahmed@ju.edu.sa

Mathematics Department, Faculty of Science,
Hassiba Benbouali, University of Chlef,
B.P. 151 Hay Essalem, Chlef 02000,
Algeria.
E-mail: benali4848@gmail.com

Abstract:

Let H be a Hilbert space and let A be a positive bounded operator on H. The semi-inner product < u|v>_A:=<Au|v>, u,v ∈ H induces a semi-norm || .||_A on H. This makes H into a semi-Hilbertian space. In this paper we introduce the notions of hyponormalities and k-quasi-hyponormalities for operators on semi Hilbertian space (H,||.||_A), based on the works that studied normal, isometry, unitary and partial isometries operators in these spaces. Also, we generalize some results which are already known for hyponormal and quasi-hyponormal operators. An operator T ∈ B_A (H) is said to be (A, k)-quasi-hyponormal if

Paper's Title:

Some criteria for Subspace-hypercyclicity of C₀-semigroups

Author(s):

Mansooreh Moosapoor

Department of Mathematics,
Farhangian University, Tehran,
Iran.
E-mail: m.mosapour@cfu.ac.ir
mosapor110@gmail.com
 

Abstract:

We research subspace-hypercyclic C₀-semigroups in this paper. We present various types of subspace-hypercyclicity criteria for C₀-semigroups. Some of them are stronger than the criteria introduced before. Also, we state that if a C₀-semigroup (T_t}_{t≥ 0} satisfies in any of them, then (T_t⊕T_t}_{t≥ 0} is subspace-hypercyclic.

Paper's Title:

A-Normal Operators In Semi Hilbertian Spaces

Author(s):

A. Saddi

Department of Mathematics,
College of Education for Girls in Sarat Ebeidah 61914, Abha,
King Khalid University
Saudi Arabia
adel.saddi@fsg.rnu.tn
 

Abstract:

In this paper we study some properties and inequalities of A-normal operators in semi-Hilbertian spaces by employing some known results for vectors in inner product spaces. We generalize also most of the inequalities of (α,β)-normal operators discussed in Hilbert spaces [7].

Paper's Title:

Sharp Inequalities Between Hölder and Stolarsky Means of Two Positive Numbers

Author(s):

M. Bustos Gonzalez and A. I. Stan

The University of Iowa,
Department of Mathematics,
14 MacLean Hall,
Iowa City, Iowa,
USA.
E-mail: margarita-bustosgonzalez@uiowa.edu
 
The Ohio State University at Marion,
Department of Mathematics,
1465 Mount Vernon Avenue,
Marion, Ohio,
USA.
E-mail: stan.7@osu.edu

Abstract:

Given any index of the Stolarsky means, we find the greatest and least indexes of the H\"older means, such that for any two positive numbers, the Stolarsky mean with the given index is bounded from below and above by the Hölder means with those indexes, of the two positive numbers. Finally, we present a geometric application of this inequality involving the Fermat-Torricelli point of a triangle.

Paper's Title:

Preserver of Local Spectrum of Skew-product Operators

Author(s):

Rohollah Parvinianzadeh^1,*, Meysam Asadipour² and Jumakhan Pazhman³

¹Department of Mathematics,
College of Sciences,
University of Yasouj,
Yasouj, 75918-74934,
Iran.
E-mail: r.parvinian@yu.ac.ir

²Department of Mathematics,
College of Sciences,
University of Yasouj,
Yasouj, 75918-74934,
Iran.
E-mail: Asadipour@yu.ac.ir

³Department of Mathematics,
Ghor Institute of higher education,
Afghanistan.
E-mail: jumapazhman@gmail.com

Abstract:

Let H and K be infinite-dimensional complex Hilbert spaces, and B(H) (resp. B(K)) be the algebra of all bounded linear operators on H (resp. on K). For an operator T∈ B(H) and a vector h∈ H, let σ_T(h) denote the local spectrum of T at h. For two nonzero vectors h₀∈ H and k₀∈ K, we show that if two maps φ₁ and φ₂ from B(H) into B(K) satisfy

σ_{φ1(T)φ2(S)*}(k₀)= σ_TS*(h₀})

for all T, S ∈ B(H), and their range containing all operators of rank at most two, then there exist bijective linear maps P : H→ K and Q : K→ H such that φ₁(T) = PTQ and φ₂(T)^* =Q^-1T^*P^-1 for all T ∈ B(H). Also, we obtain some interesting results in this direction.

Paper's Title:

Boundedness for Vector-Valued Multilinear Singular Integral Operators on Triebel-Lizorkin Spaces

Author(s):

Liu Lanzhe

College of Mathematics
Changsha University of Science and Technology,
Changsha 410077,
P.R. of China.
lanzheliu@263.net

Abstract:

In this paper, the boundedness for some vector-valued multilinear operators associated to certain fractional singular integral operators on Triebel-Lizorkin space are obtained. The operators include Calderón-Zygmund singular integral operator and fractional integral operator.

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