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2 Demonstratio Mathematica

2 2013

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Product of weighted Hankel and weighted Toeplitz operators

Datt G., Porwal D. K.

Demonstratio Mathematica

2013

Vol. 46, nr 3

571--583

In this paper, we discuss some properties of the weighted Hankel operator H(...) and describe the conditions on which the weighted Hankel operator H(...) and weighted Toeplitz operator T(...), with (…) on the space H(...) being a sequence of positive numbers with (…), commute. It is also proved that if a non-zero weighted Hankel operator H(...) commutes with T(...), which is not a multiple of the identity, then H(...), for some (…).

Injective composition operators on Lorentz-Bochner spaces

Datt G., Arora S. C.

Demonstratio Mathematica

2013

Vol. 46, nr 4

741--756

In this paper, we extend the notion of essential range to vector-valued functions and present various equivalent conditions for the injectiveness of the composition operators alongwith a characterisation for measurable transformations inducing composition operators between Lorentz-Bochner spaces. Some aspects of the weighted composition operators on Lorentz-Bochner spaces, induced by a measurable transformation and an operator valued map, are also discussed.