P. S. Johnson

Lipschitz p-Approximate Schauder Frames

K. Mahesh Krishna, P. Sam Johnson

With the aim of representing subsets of Banach spaces as an infinite series using Lipschitz functions, we study a variant of metric frames which we call Lipschitz p-approximate Sch…

Controlled continuous $g$ -frames and their duals in Hilbert spaces

Mohamed Rossafi, Fakhr-dine Nhari, P. Sam Johnson

In this paper, we characterize and study the concept of controlled continuous $g$ -frame which is an extension of continuous $g$ -frame in Hilbert spaces. We introduce the concept of…

Reverse Order Law for Closed Range Operators in Hilbert Spaces

Athira Satheesh K., K. Kamaraj, P. Sam Johnson

We present more than 50 results including some range inclusion results to characterize reverse order law for Moore-Penrose inverse of closed range Hilbert space operators. We use b…

P-Operators on Hilbert Spaces

Rashid A., P. Sam Johnson

A real square matrix $A$ is called a P-matrix if all its principal minors are positive. Using the sign non-reversal property of matrices, the notion of P-matrix has been recently e…

Operator-Valued p-Approximate Schauder Frames

K. Mahesh Krishna, P. Sam Johnson

We give an operator-algebraic treatment of theory of p-approximate Schuader frames which includes the theory of operator-valued frames by Kaftal, Larson, and Zhang [\textit{Trans.…

Approximately Dual p-Approximate Schauder Frames

K. Mahesh Krishna, P. Sam Johnson

Difficulty in the construction of dual frames for a given Hilbert space led to the introduction of approximately dual frames in Hilbert spaces by Christensen and Laugesen. It becom…

Closed $E P$ and Hypo- $E P$ Operators on Hilbert Spaces

P. Sam Johnson

A bounded linear operator $A$ on a Hilbert space $H$ is said to be an $E P$ (hypo- $E P$ ) operator if ranges of $A$ and $A^{*}$ are equal (range of $A$ is containe…

Generalized Principal Pivot Transform and its Inheritance Properties

K. Kamaraj, P. Sam Johnson, Sachin Manjunath Naik

In this paper, some more properties of the generalized principal pivot transform are derived. Necessary and sufficient conditions for the equality between Moore-Penrose inverse of…

Reverse Order Law for Generalized Inverses with Indefinite Hermitian Weights

K. Kamaraj, P. Sam Johnson, Athira Satheesh

In this paper, necessary and sufficient conditions are given for the existence of Moore-Penrose inverse of a product of two matrices in an indefinite inner product space (IIPS) in…

Dilations of Linear Maps on Vector Spaces

K. Mahesh Krishna, P. Sam Johnson

We continue the study dilation of linear maps on vector spaces introduced by Bhat, De, and Rakshit. This notion is a variant of vector space dilation introduced by Han, Larson, Liu…

math.OA2021

Commutators Close to the Identity in Unital C*-Algebras

K. Mahesh Krishna, P. Sam Johnson

Let $H$ be an infinite dimensional Hilbert space and $B (H)$ be the C*-algebra of all bounded linear operators on $H$ , equipped with the oper…

Expansion of approximate Bessel sequences to approximate Schauder frames for Banach spaces

K. Mahesh Krishna, P. Sam Johnson

It is known in Hilbert space frame theory that a Bessel sequence can be expanded to a frame. Contrary to Hilbert space situation, using a result of Casazza and Christensen, we show…

math.FA2021★ 1 cited

Fuglede-Putnam type commutativity theorems for $E P$ operators

P. Sam Johnson, Vinoth A., K. Kamaraj

Fuglede-Putnam theorem is not true in general for $E P$ operators on Hilbert spaces. We prove that under some conditions the theorem holds good. If the adjoint operation is replac…

New Identity on Parseval p-Approximate Schauder Frames and Applications

K. Mahesh Krishna, P. Sam Johnson

A very useful identity for Parseval frames for Hilbert spaces was obtained by Balan, Casazza, Edidin, and Kutyniok. In this paper, we obtain a similar identity for Parseval p-appro…

Perturbation of p-approximate Schauder frames for separable Banach spaces

K. Mahesh Krishna, P. Sam Johnson

Paley-Wiener theorem for frames for Hilbert spaces, Banach frames, Schauder frames and atomic decompositions for Banach spaces are known. In this paper, we derive Paley-Wiener theo…

math.FA2020★ 2 cited

Dilation theorem for p-approximate Schauder frames for separable Banach spaces

K. Mahesh Krishna, P. Sam Johnson

Famous Naimark-Han-Larson dilation theorem for frames in Hilbert spaces states that every frame for a separable Hilbert space $H$ is image of a Riesz basis under an ortho…

Factorable Weak Operator-Valued Frames

K. Mahesh Krishna, P. Sam Johnson

Let $H$ and $H_{0}$ be Hilbert spaces and ${A_{n}}_{n}$ be a sequence of bounded linear operators from $H$ to $H_{0}$ . The study frames for Hilber…

math.FA2020★ 1 cited

Estimates of Norms on Krein Spaces

Athira Satheesh K., P. Sam Johnson, K. Kamaraj

Various norms can be defined on a Krein space by choosing different underlying fundamental decompositions. Some estimates of norms on Krein spaces are discussed and few results in…

Frames for Metric Spaces

K. Mahesh Krishna, P. Sam Johnson

We make a systematic study of frames for metric spaces. We prove that every separable metric space admits a metric $M_{d}$ -frame. Through Lipschitz-free Banach spaces we sh…