caa a22 4500 60550881X CHVBK 20210128100638.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s00010-014-0293-3 doi (NATIONALLICENCE)springer-10.1007/s00010-014-0293-3 Wójcik Paweł Institute of Mathematics, Pedagogical University of Cracow, Podchor֥ażych 2, 30-084, Kraków, Poland aut Characterizations of smooth spaces by approximate orthogonalities [Elektronische Daten] [Paweł Wójcik] Since the monograph by Amir that appeared in 1986, a lot of attention has been given to the problem of characterizing, by means of properties of the norms, when a Banach space is indeed a Hilbert space, i.e., when the norm derives from an inner product. In this paper, similar investigations will be carried out for smooth spaces instead of inner product spaces. We consider the approximate orthogonalities in real normed spaces. We show that the relations approximate semi-orthogonality and approximate ρ+-orthogonality are generally incomparable (unless the normed space is smooth). As a result, we give a characterization of smooth spaces in terms of those approximate orthogonalities. The Author(s), 2014 Approximate orthogonality nationallicence Smoothness nationallicence Norm derivative nationallicence Semi-inner product nationallicence Aequationes mathematicae Springer Basel 89/4(2015-08-01), 1189-1194 0001-9054 89:4<1189 2015 89 10 https://doi.org/10.1007/s00010-014-0293-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-014-0293-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Wójcik Paweł Institute of Mathematics, Pedagogical University of Cracow, Podchor֥ażych 2, 30-084, Kraków, Poland aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/4(2015-08-01), 1189-1194 0001-9054 89:4<1189 2015 89 10