Some properties of the matrix class (ℓα, ℓα), 0 < α ⩽ 1

• Autorzy: Natarajan, Pinnangudi N.
• Języki publikacji: EN

Abstrakty

EN

Throughout the present paper, entries of sequences, infinite series and infinite matrices are real or complex numbers. The class (ℓ_α, ℓ_α), 0 < α ⩽ 1, of all infinite matrices transforming sequences in ℓ_α to sequences in ℓ_α is characterized. The structure of (ℓ_α, ℓ_α), 0 < α ⩽ 1, is then discussed. Following Fridy [Properties of absolute summability matrices, Proc. Amer. Math. Soc. 24 (1970), 583-585], a Steinhaus type result involving the class (ℓ_α, ℓ_α) is also proved.

Słowa kluczowe

EN

A-transform; Cauchy product; α-norm; α-normed linear space; Steinhaus type theorem

• Czasopismo: Commentationes Mathematicae
• Rocznik: 2020
• Tom: Vol. 60, No. 1/2
• Strony: 23--36
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Natarajan, Pinnangudi N.

• Old No. 2/3, New No. 3/3, Second Main Road, R.A. Puram, Chennai 600 028, India,

Bibliografia

• [1] J. A. Fridy, A note on absolute summability, Proc. Amer. Math. Soc. 20 (1969), 285-286, DOI 10.2307/2036011.
• [2] J. A. Fridy, Properties of absolute summability matrices, Proc. Amer. Math. Soc. 24 (1970), 583-585, DOI 10.2307/2037413.
• [3] K. Knopp and G. G. Lorentz, Beiträge zur absoluten Limitierung, Arch. Math. 2 (1949), 10-16, DOI 10.1007/BF02036747.
• [4] M. Koskela, A characterization of non-negative matrix operators on lp to lq with ∞ > p ⩾ q > 1, Pacific J. Math. 75 (1978), no. 1, 165-169.
• [5] I. J. Maddox, Elements of functional analysis, Cambridge University Press, London – New York 1970.
• [6] F. M. Mears, Absolute regularity and the Nörlund mean, Ann. of Math. (2) 38 (1937), no. 3, 594-601, DOI 10.2307/1968603.
• [7] I. Schur, Über lineare Transformationen in der Theorie der unendlichen Reihen, J. Reine Angew. Math. 151 (1921), 79-111, DOI 10.1515/crll.1921.151.79.
• [8] M. Stieglitz and H. Tietz, Matrixtransformationen von Folgenräumen. Eine Ergebnisübersicht, Math. Z. 154 (1977), no. 1, 1-16, DOI 10.1007/BF01215107.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).

Identyfikatory

DOI

10.14708/cm.v60i1-2.7044