Том 71
№ 11

All Issues

Gupta S.

Articles: 3
Brief Communications (English)

On the β-Dual of Banach-Space-Valued Difference Sequence Spaces

Bhardwaj V. K., Gupta S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 8. - pp. 1145–1151

The main object of the paper is to introduce Banach-space-valued difference sequence spaces (X, Δ), c(X, Δ); and c0(X, Δ) as a generalization of the well-known difference sequence spaces of Kizmaz. We obtain a set of sufficient conditions for (A k ) ∈ E β (X, Δ); where E ∈ { , c, c 0} and (A k ) is a sequence of linear operators from a Banach space X into another Banach space Y: Necessary conditions for (A k ) ∈ E β (X, Δ) are also investigated.

Brief Communications (English)

On 2-Symmetric Words in Nilpotent Groups

Gupta S., Holubowski W.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 7. - pp. 1020-1024

We find the nilpotency class of a group of 2-symmetric words for free nilpotent groups, free nilpotent metabelian groups, and free (nilpotent of class c)-by-Abelian groups.

Article (Ukrainian)

A Presentation of the Automorphism Group of the Two-Generator Free Metabelian and Nilpotent Group of Class $c$

Gupta S., Wan Lin

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 6. - pp. 771-779

We determine the structure of IA(G)/Inn(G) by giving a set of generators, and showing that IA(G)/Inn(G) is a free abelian group of rank (c − 2)(c + 3)/2. Here G = M 2, c = 〈 x, y〉, c ≥ 2, is the free metabelian nilpotent group of class c.