Hypo-q-Norms on a Cartesian Product of Algebras of Operators on Banach Spaces

• Autorzy: Sever Silvestru Dragomir
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider the hypo-q-operator norm and hypo-q-numerical radius on a Cartesian product of algebras of bounded linear operators on Banach spaces. A representation of these norms in terms of semi-inner products, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar reverses of Cauchy-Buniakowski-Schwarz inequality are also given. (original abstract)

Słowa kluczowe

EN

Mathematics; Mathematical inequalities; Set theory

PL

Matematyka; Nierówności matematyczne; Teoria zbiorów

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2020
• Tom: 34 (2)
• Strony: 169--192

Twórcy

autor

Sever Silvestru Dragomir

• Victoria University, Australia

Bibliografia

• S.S. Dragomir, A survey on Cauchy-Bunyakovsky-Schwarz type discrete inequalities, J. Inequal. Pure Appl. Math. 4 (2003), no. 3, Art. 63, 142 pp. Available at https://www.emis.de/journals/JIPAM/article301.html?sid=301.
• S.S. Dragomir, A counterpart of Schwarz's inequality in inner product spaces, East Asian Math. J. 20 (2004), no. 1, 1-10. Preprint RGMIA Res. Rep. Coll. 6 (2003), Supplement, Art. 18. Available at http://rgmia.org/papers/v6e/CSIIPS.pdf.
• S.S. Dragomir, Semi-Inner Products and Applications, Nova Science Publishers, Inc., Hauppauge, NY, 2004.
• S.S. Dragomir, Advances in Inequalities of the Schwarz, Grüss and Bessel Type in Inner Product Spaces, Nova Science Publishers, Inc., Hauppauge, NY, 2005.
• S.S. Dragomir, Reverses of the Schwarz inequality generalising a Klamkin-McLenaghan result, Bull. Austral. Math. Soc. 73 (2006), no. 1, 69-78.
• S.S. Dragomir, The hypo-Euclidean norm of an n-tuple of vectors in inner product spaces and applications, J. Inequal. Pure Appl. Math. 8 (2007), no. 2, Art. 52, 22 pp. Available at https://www.emis.de/journals/JIPAM/article854.html?sid=854.
• S.S. Dragomir, Hypo-q-norms on a Cartesian product of normed linear spaces, Preprint RGMIA Res. Rep. Coll. 20 (2017), Art. 153. Available at http://rgmia.org/papers/v20/v20a153.pdf.
• S.S. Dragomir, Inequalities for hypo-q-norms on a Cartesian product of inner product spaces, Preprint RGMIA Res. Rep. Coll. 20 (2017), Art. 168. Available at http://rgmia.org/papers/v20/v20a168.pdf.
• J.R. Giles, Classes of semi-inner-product spaces, Trans. Amer. Math. Soc. 129 (1967), 436-446.
• B.W. Glickfeld, On an inequality of Banach algebra geometry and semi-inner product space theory, Illinois J. Math. 14 (1970), 76-81.
• G. Lumer, Semi-inner-product spaces, Trans. Amer. Math. Soc. 100 (1961), 29-43.
• P.M. Miličić, Sur le semi-produit scalaire dans quelques espaces vectoriels normés, Mat. Vesnik 8(23) (1971), 181-185.
• P.M. Miličić, Une généralisation naturelle du produit scalaire dans un espace normé et son utilisation, Publ. Inst. Math. (Beograd) (N.S.) 42(56) (1987), 63-70.
• P.M. Miličić, La fonctionelle g et quelques problèmes des meilleures approximations dans des espaces normés, Publ. Inst. Math. (Beograd) (N.S.) 48(62) (1990), 110-118.
• M.S. Moslehian, M. Sattari and K. Shebrawi, Extensions of Euclidean operator radius inequalities, Math. Scand. 120 (2017), no. 1, 129-144.
• B. Nath, On a generalization of semi-inner product spaces, Math. J. Okayama Univ. 15 (1971), no. 1, 1-6.
• P.L. Papini, Un'osservazione sui prodotti semi-scalari negli spazi di Banach, Boll. Un. Mat. Ital. (4) 2 (1969), 686-689.
• I. Roşca, Semi-produit scalaire et représentations de type de Riesz pour les fonctionelles linéaires et bornées sur les espaces normés, C.R. Acad. Sci. Paris Sér. A-B 283 (1976), no. 3, Ai, A79-A81.
• O. Shisha and B. Mond, Bounds on differences of means, in: O. Shisha (ed.), Inequalities, Academic Press, Inc., New York, 1967, pp. 293-308.

Identyfikatory

DOI

10.2478/amsil-2019-0014