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  1. Mediterranean Journal of Mathematics
  2. Mediterranean Journal of Mathematics : Volume 10
  3. Mediterranean Journal of Mathematics : Volume 10, Issue 1, February 2013
  4. A Note on Quasi-paranormal Operators
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Mediterranean Journal of Mathematics : Volume 14
Mediterranean Journal of Mathematics : Volume 13
Mediterranean Journal of Mathematics : Volume 12
Mediterranean Journal of Mathematics : Volume 11
Mediterranean Journal of Mathematics : Volume 10
Mediterranean Journal of Mathematics : Volume 10, Issue 4, November 2013
Mediterranean Journal of Mathematics : Volume 10, Issue 3, August 2013
Mediterranean Journal of Mathematics : Volume 10, Issue 2, May 2013
Mediterranean Journal of Mathematics : Volume 10, Issue 1, February 2013
A Weighted Generalization of the Classical Kantorovich Operator. II: Saturation
Complete Asymptotic Expansions for Altomare Operators
Approximation by Complex Beta Operators of First Kind in Strips of Compact Disks
On Convergence of Chlodovsky and Chlodovsky–Kantorovich Polynomials in the Variation Seminorm
Explicit Formulas and Combinatorial Identities for Generalized Stirling Numbers
On Extending $${\mathcal{A}}$$ -Modules Through the Coefficients
On a Quadratic Eigenvalue Problem and its Applications
Nil-Armendariz Rings Relative to a Monoid
Power Values of Generalized Derivations with Annihilator Conditions in Prime Rings
The Yagita Invariant of Some Symplectic Groups
On the Oscillation of nth Order Dynamic Equations on Time-Scales
Laplace Equation on a Domain With a Cuspidal Point in Little Hölder Spaces
Some Results on Stability and Stabilization of Homogeneous Time-Varying Systems
Exact Multiplicity and Stability of Periodic Solutions for a Duffing Equation
Approximate Weak Invariance and Relaxation for Fully Nonlinear Differential Inclusions
A New Class of Kernels Leading to an Arbitrary Decay in Viscoelasticity
Determination of the Unknown Cauchy Data in a Linear Parabolic Problem from the Measured Data at the Final Time
Uniform Boundedness and Decay Estimates for a System of Reaction-Diffusion Equations with a Triangular Diffusion Matrix on $${\mathbb{R}^{n}}$$
Existence Result for Triangular Reaction—Diffusion Systems with L1 Data and Critical Growth with Respect to the Gradient
Discontinuous Boundary Value Problems with Retarded Argument and Eigenparameter-Dependent Boundary Conditions
Strong Regularizing Effect of a Gradient Term in the Heat Equation with a Weight
A Sharp Inequality for a Trigonometric Sum
Generalized Frames in the Space of Strong Limit Power Functions
Uncertainty Inequalities on Laguerre Hypergroup
The Continuous Zak Transform and Generalized Gabor Frames
Property (R) under Perturbations
A Note on Quasi-paranormal Operators
Weighted Composition Operators from the Minimal Möbius Invariant Space into the Bloch Space
On Two-sided Locally Convex H*-algebras
On Lineability in Vector Integration
The Geometry of Elation Groups of a Finite Projective Space
On Transversally Elliptic Operators and the Quantization of Manifolds with f-Structure
Generalized $${{(\kappa, \mu)}}$$ -Space Forms
Minimal and Pseudo-Umbilical Rotational Surfaces in Euclidean Space $${\mathbb{E}^4}$$
A Symmetry Result on Submanifolds of Space Forms and Applications
On 2-dimensional Nonaspherical Cell-like Peano Continua: A Simplified Approach
Bornological Convergence and Shields
Knots with the Lens Space Surgery
Affine Biharmonic Curves in 3-Dimensional Homogeneous Geometries
On the Calculus of Limiting Subjets on Riemannian Manifolds
Erratum to “Frames for Weighted Shift-Invariant Spaces", Mediterr. J. Math., DOI:10.1007/s00009-011-0155-3
Mediterranean Journal of Mathematics : Volume 9
Mediterranean Journal of Mathematics : Volume 8
Mediterranean Journal of Mathematics : Volume 7
Mediterranean Journal of Mathematics : Volume 6
Mediterranean Journal of Mathematics : Volume 5
Mediterranean Journal of Mathematics : Volume 4
Mediterranean Journal of Mathematics : Volume 3
Mediterranean Journal of Mathematics : Volume 2
Mediterranean Journal of Mathematics : Volume 1

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A Note on Quasi-paranormal Operators

Content Provider SpringerLink
Author Na, Won Hee Han, Young Min
Copyright Year 2012
Abstract Let T be a bounded linear operator on an infinite dimensional complex Hilbert space. In this paper, we introduce the new class, denoted $${{\mathcal{QP}}}$$ , of operators satisfying $${{\|T^{2}x\|^{2}\leq \|T^{3}x\|\|Tx\|}}$$ for all $${{x \in \mathcal{H}}}$$ . This class includes the classes of paranormal operators and quasi-class A operators. We prove basic structural properties of these operators. Using these results, we also prove that if E is the Riesz idempotent for a nonzero isolated point λ0 of the spectrum of $${{T \in \mathcal{QP}}}$$ , then E is self-adjoint if and only if $${{N(T-\lambda_{0}) \subseteq N(T^{*}-\overline{\lambda}_{0})}}$$ .
Ending Page 393
Page Count 11
Starting Page 383
File Format PDF
ISSN 16605446
e-ISSN 16605454
Journal Mediterranean Journal of Mathematics
Issue Number 1
Volume Number 10
Language English
Publisher SP Birkhäuser Verlag Basel
Publisher Date 2012-01-12
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword algebraically quasi paranormal operator Quasi-paranormal operator Spectrum, resolvent Bishop’s property (β) Subnormal operators, hyponormal operators, etc. SVEP Mathematics Local spectral properties
Content Type Text
Resource Type Article
Subject Mathematics
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