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

[1] 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.Search in Google Scholar

[2] 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.Search in Google Scholar

[3] S.S. Dragomir, Semi-Inner Products and Applications, Nova Science Publishers, Inc., Hauppauge, NY, 2004.Search in Google Scholar

[4] S.S. Dragomir, Advances in Inequalities of the Schwarz, Grüss and Bessel Type in Inner Product Spaces, Nova Science Publishers, Inc., Hauppauge, NY, 2005.Search in Google Scholar

[5] S.S. Dragomir, Reverses of the Schwarz inequality generalising a Klamkin-McLenaghan result, Bull. Austral. Math. Soc. 73 (2006), no. 1, 69–78.Search in Google Scholar

[6] 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.Search in Google Scholar

[7] 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.10.20944/preprints201711.0097.v1Search in Google Scholar

[8] 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.10.20944/preprints201711.0097.v1Search in Google Scholar

[9] J.R. Giles, Classes of semi-inner-product spaces, Trans. Amer. Math. Soc. 129 (1967), 436–446.10.1090/S0002-9947-1967-0217574-1Search in Google Scholar

[10] B.W. Glickfeld, On an inequality of Banach algebra geometry and semi-inner product space theory, Illinois J. Math. 14 (1970), 76–81.10.1215/ijm/1256053302Search in Google Scholar

[11] G. Lumer, Semi-inner-product spaces, Trans. Amer. Math. Soc. 100 (1961), 29–43.10.1090/S0002-9947-1961-0133024-2Search in Google Scholar

[12] P.M. Miličić, Sur le semi-produit scalaire dans quelques espaces vectoriels normés, Mat. Vesnik 8(23) (1971), 181–185.Search in Google Scholar

[13] 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.Search in Google Scholar

[14] 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.Search in Google Scholar

[15] M.S. Moslehian, M. Sattari and K. Shebrawi, Extensions of Euclidean operator radius inequalities, Math. Scand. 120 (2017), no. 1, 129–144.Search in Google Scholar

[16] B. Nath, On a generalization of semi-inner product spaces, Math. J. Okayama Univ. 15 (1971), no. 1, 1–6.Search in Google Scholar

[17] P.L. Papini, Un’osservazione sui prodotti semi-scalari negli spazi di Banach, Boll. Un. Mat. Ital. (4) 2 (1969), 686–689.Search in Google Scholar

[18] 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.Search in Google Scholar

[19] O. Shisha and B. Mond, Bounds on differences of means, in: O. Shisha (ed.), Inequalities, Academic Press, Inc., New York, 1967, pp. 293–308.Search in Google Scholar