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A REMARK ON SOME INEQUALITIES FOR THE SCHATTEN p-NORM
HEDAYATIAN, K.,BAHMANI, F. The Honam Mathematical Society 2002 호남수학학술지 Vol.24 No.1
For a closed densely defined linear operator T on a Hilbert space H, let ${\prod}$ denote the function which corresponds to T, the orthogonal projection from $H{\oplus}H$ onto the graph of T. We extend some ordinary norm ineqralites comparing ${\parallel}{\Pi}(A)-{\Pi}(B){\parallel}$ and ${\parallel}A-B{\parallel}$ to the Schatten p-norm where A and B are bounded operators on H.
Isometries on the space of continuous functions with finite codimensional range
Hedayatian, K. 호남수학회 2005 호남수학학술지 Vol.27 No.4
For compact Hausdorff spaces X and Y let C(X) and C(Y ) denote the complex Banach spaces of complex valued continuous functions on X and Y , respectively. Also let T : C(X) C(Y )→be a linear isomerty. Necessary and sufficient conditions are given such that range of T has finite codimension.
SOME PROPERTIES OF INVARIANT SUBSPACES IN BANACH SPACES OF ANALYTIC FUNCTIONS
Hedayatian, K.,Robati, B. Khani The Honam Mathematical Society 2007 호남수학학술지 Vol.29 No.4
Let $\cal{B}$ be a reflexive Banach space of functions analytic on the open unit disc and M be an invariant subspace of the multiplication operator by the independent variable, $M_z$. Suppose that $\varphi\;\in\;\cal{H}^{\infty}$ and $M_{\varphi}$ : M ${\rightarrow}$ M, defined by $M_{\varphi}f={\varphi}f$, is the operator of multiplication by ${\varphi}$. We would like to investigate the spectrum and the essential spectrum of $M_{\varphi}$ and we are looking for the necessary and sufficient conditions for $M_{\varphi}$ to be a Fredholm operator. Also we give a sufficient condition for a sequence $\{w_n\}$ to be an interpolating sequence for $\cal{B}$. At last the commutant of $M_{\varphi}$ under certain conditions on M and ${\varphi}$ is determined.
ON A CLASS OF REFLEXIVE TOEPLITZ OPERATORS
HEDAYATIAN, K. The Honam Mathematical Society 2006 호남수학학술지 Vol.28 No.4
We will use a result of Farrell, Rubel and Shields to give sufficient conditions under which a Toeplitz operator with conjugate analytic symbol to be reflexive on Dirichlet-type spaces.
N-SUPERCYCLICITY OF AN A-m-ISOMETRY
HEDAYATIAN, KARIM The Honam Mathematical Society 2015 호남수학학술지 Vol.37 No.3
An A-m-isometric operator is a bounded linear operator T on a Hilbert space $\mathcal{H}$ satisfying $\sum\limits_{k=0}^{m}(-1)^{m-k}T^{*^k}AT^k=0$, where A is a positive operator. We give sufficient conditions under which A-m-isometries are not N-supercyclic, for every $N{\geq}1$; that is, there is not a subspace E of dimension N such that its orbit under T is dense in $\mathcal{H}$.
POWER REGULARITY OF ISOMETRIC N-JORDAN OPERATORS
Hedayatian, Karim,Yarmahmoodi, Saeed The Honam Mathematical Society 2016 호남수학학술지 Vol.38 No.2
In this paper, we show that for every $N{\in}\mathbb{N}$, isometric N-Jordan operators on Hilbert spaces are power regular. Moreover, the only normaloid or 2-isometric, N-Jordan operators are isometries.
Supercyclicity of Convex Operators
Hedayatian, Karim,Karimi, Lotfollah Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.1
A bounded linear operator T on a Hilbert space ${\mathcal{H}}$ is convex, if for each $x{\in}{\mathcal{H}}$, ${\parallel}T^2x{\parallel}^2-2{\parallel}Tx{\parallel}^2+{\parallel}x{\parallel}^2{\geq}0$. In this paper, it is shown that if T is convex and supercyclic then it is a contraction or an expansion. We then present some examples of convex supercyclic operators. Also, it is proved that no convex composition operator induced by an automorphism of the disc on a weighted Hardy space is supercyclic.
Some Properties of Invariant Subsoaces in Banach Spaces of Analytic Functions
K.Hedayatian,B. Khani Robati 호남수학회 2007 호남수학학술지 Vol.29 No.4
LetB be a reexive Banach space of functions analyticon the open unit disc and M be an invariant subspace of the multi-plication operator by the independent variable, M z. Suppose that' 2 H1 and M ' :M ! M , dened byM ' f = 'f , is the operatorof multiplication by '. We would like to investigate the spectrumand the essential spectrum ofM ' and we are looking for the nec-essary and sucient conditions forM ' to be a Fredholm operator.Also we give a sucient condition for a sequencef! n g to be aninterpolating sequence forB. At last the commutant ofM ' undercertain conditions on M and ' is determined.