K. Thirulogasanthar
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View article: Berberian extension and its S-spectra in a quaternionic Hilbert space
Berberian extension and its S-spectra in a quaternionic Hilbert space Open
For a bounded right linear operators $A$, in a right quaternionic Hilbert space $V_{\mathbb{H}}^{R}$, following the complex formalism, we study the Berberian extension $A^\circ$, which is an extension of $A$ in a right quaternionic Hilbert…
View article: Perturbation of Continuous Frames on Quaternionic Hilbert Spaces
Perturbation of Continuous Frames on Quaternionic Hilbert Spaces Open
In this note, following the theory of discrete frame perturbations in a complex Hilbert space, we examine perturbation of rank $n$ continuous frame, rank $n$ continuous Bessel family and rank $n$ continuous Riesz family in a non-commutativ…
View article: Decomposable operators, local S-spectrum and S-spectrum in the quaternionic setting
Decomposable operators, local S-spectrum and S-spectrum in the quaternionic setting Open
In a right quaternionic Hilbert space, following the complex formalism, decomposable operators, the so-called Bishop's property and the single valued extension property are defined and the connections between them are studied to certain ex…
View article: Kato S-spectrum in the quaternionic setting
Kato S-spectrum in the quaternionic setting Open
In a right quaternionic Hilbert space, for a bounded right linear operator, the Kato S-spectrum is introduced and studied to a certain extent. In particular, it is shown that the Kato S-spectrum is a non-empty compact subset of the S-spect…
View article: Fredholm operators and essential S-spectrum in the quaternionic setting
Fredholm operators and essential S-spectrum in the quaternionic setting Open
For bounded right linear operators, in a right quaternionic Hilbert space with a left multiplication defined on it, we study the approximate S-point spectrum. In the same Hilbert space, then we study the Fredholm operators and the Fredholm…
View article: Frame Multipliers for discrete frames on Quaternionic Hilbert Spaces
Frame Multipliers for discrete frames on Quaternionic Hilbert Spaces Open
In this note, following the complex theory, we examine discrete controlled frames, discrete weighted frames and frame multipliers in a non-commutative setting, namely in a left quaternionic Hilbert space. In particular, we show that the co…
View article: Lagrange Multiplier Local Necessary and Global Sufficiency Criteria for Some Non-Convex Programming Problems
Lagrange Multiplier Local Necessary and Global Sufficiency Criteria for Some Non-Convex Programming Problems Open
In this paper we consider three minimization problems, namely quadratic, $ρ$-convex and quadratic fractional programing problems. The quadratic problem is considered with quadratic inequality constraints with bounded continuous and discret…
View article: Squeezed states in the quaternionic setting
Squeezed states in the quaternionic setting Open
Using a left multiplication defined on a right quaternionic Hilbert space, we shall demonstrate that pure squeezed states can be defined with all the desired properties on a right quaternionic Hilbert space. Further, we shall also demonstr…
View article: General construction of reproducing kernels on a quaternionic Hilbert space
General construction of reproducing kernels on a quaternionic Hilbert space Open
A general theory of reproducing kernels and reproducing kernel Hilbert spaces on a right quaternionic Hilbert space is presented. Positive operator-valued measures and their connection to a class of generalized quaternionic coherent states…
View article: Coherent states on quaternion Slices and a measurable field of Hilbert spaces
Coherent states on quaternion Slices and a measurable field of Hilbert spaces Open
A set of reproducing kernel Hilbert spaces are obtained on Hilbert spaces over quaternion slices with the aid of coherent states. It is proved that the so obtained set forms a measurable field of Hilbert spaces and their direct integral ap…