Browsing Mathematics (MA) by Advisor "Misra, Gadadhar"
Now showing items 1-14 of 14
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Analytic Models, Dilations, Wandering Subspaces and Inner Functions
This thesis concerns dilation theory, analytic models, joint invariant subspaces, reproducing kernelHilbert spaces and multipliers associated to commuting tuples of bounded linear operators on Hilbert spaces. The main ... -
The Caratheodory-Fejer Interpolation Problems and the Von-Neumann inequality
(2018-05-30)The validity of the von-Neumann inequality for commuting $n$ - tuples of $3\times 3$ matrices remains open for $n\geq 3$. We give a partial answer to this question, which is used to obtain a necessary condition for the ... -
Curvature Calculations Of The Operators In Cowen-Douglas Class
(2014-03-03)In a foundational paper “Operators Possesing an Open Set of Eigenvalues” written several decades ago, Cowen and Douglas showed that an operator T on a Hilbert space ‘H possessing an open set Ω C of eigenvalues determines ... -
Decomposition of the tensor product of Hilbert modules via the jet construction and weakly homogeneous operators
Let ½ Cm be a bounded domain and K :£!C be a sesqui-analytic function. We show that if ®,¯ È 0 be such that the functions K® and K¯, defined on £, are non-negative definite kernels, then theMm(C) valued function ... -
Geometric invariants for a class of submodules of analytic Hilbert modules
Let $\Omega \subseteq \mathbb C^m$ be a bounded connected open set and $\mathcal H \subseteq \mathcal O(\Omega)$ be an analytic Hilbert module, i.e., the Hilbert space $\mathcal H$ possesses a reproducing kernel $K$, the ... -
Geometry of normed linear spaces in light of Birkhoff-James orthogonality
In this thesis, we have tried to understand the geometry of normed spaces in the light of Birkhoff-James orthogonality. Using the first two chapters to give introductory notes and to establish relevant notations and ... -
Grothendieck Inequality
(2016-06-20)Grothendieck published an extraordinary paper entitled ”Resume de la theorie metrique des pro¬duits tensoriels topologiques” in 1953. The main result of this paper is the inequality which is commonly known as Grothendieck ... -
Homogeneous Operators
(2018-06-13)A bounded operator T on a complex separable Hilbert space is said to be homogeneous if '(T ) is unitarily equivalent to T for all ' in M•ob, where M•ob is the M•obius group. A complete description of all homogeneous weighted ... -
Homogeneous Operators and Some Irreducible Representations of the Mobius Group
In this report, after recalling the definition of the M¨obius group, we define homogeneous operators, that is, operators T with the property '(T) is unitarily equivalent to T for all ' in the M¨obius group and prove some ... -
Infinitely Divisible Metrics, Curvature Inequalities And Curvature Formulae
(2014-06-30)The curvature of a contraction T in the Cowen-Douglas class is bounded above by the curvature of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. ... -
Normal Spectrum of a Subnormal Operator
(2018-03-21)Let H be a separable Hilbert space over the complex field. The class S := {N|M : N is normal on H and M is an invariant subspace for Ng of subnormal operators. This notion was introduced by Halmos. The minimal normal ... -
Subnormality and Moment Sequences
(2018-03-07)In this report we survey some recent developments of relationship between Hausdorff moment sequences and subnormality of an unilateral weighted shift operator. Although discrete convolution of two Haudorff moment sequences ... -
Trace Estimate For The Determinant Operator And K- Homogeneous Operators
Let $\boldsymbol T=(T_1, \ldots , T_d)$ be a $d$- tuple of commuting operators on a Hilbert space $\mathcal H$. Assume that $\boldsymbol T$ is hyponormal, that is, $\big [\!\!\big [ \boldsymbol T^*, \boldsymbol T \big ]\!\! ...