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Fuglede-Putnam theorem is not true in general for $ EP $ operators on Hilbert spaces. We prove that under some conditions the theorem holds good. If the adjoint operation is replaced by Moore-Penrose inverse in the theorem, we get Fuglede-Putnam type theorem for $ EP $ operators -- however proofs are totally different. Finally, interesting results on $ EP $ operators have been proved using sever
A bounded linear operator $ A$ on a Hilbert space $ mathcal H $ is said to be an $ EP $ (hypo-$ EP $) operator if ranges of $ A $ and $ A^* $ are equal (range of $ A $ is contained in range of $ A^* $) and $ A $ has a closed range. In this paper, we
This note contains a representation formula for positive solutions of linear degenerate second-order equations of the form $$ partial_t u (x,t) = sum_{j=1}^m X_j^2 u(x,t) + X_0 u(x,t) qquad (x,t) in mathbb{R}^N times, ]- infty ,T[,$$ proved by a func
The main objective of this work is to study generalized Browders and Weyls theorems for the multiplication operators $L_A$ and $R_B$ and for the elementary operator $tau_{A,B}=L_AR_B$.
In this article we introduce a new class of Rolewicz-type operators in l_p, $1 le p < infty$. We exhibit a collection F of cardinality continuum of operators of this type which are chaotic and remain so under almost all finite linear combinations, pr
In this paper we develop the theory of Fourier multiplier operators $T_{m}:L^{p}(mathbb{R}^{d};X)to L^{q}(mathbb{R}^{d};Y)$, for Banach spaces $X$ and $Y$, $1leq pleq qleq infty$ and $m:mathbb{R}^dto mathcal{L}(X,Y)$ an operator-valued symbol. The ca