Geodesic
Characterization of inner product spaces by unitary Carlsson type orthogonalities
Filomat, Tome 36 (2022) no. 14, p. 4655

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DOI

In this study, we consider the Hermite-Hadamard type of unitary Carlsson's orthogonality (UHH-C-orthogonality) to characterize real inner product spaces. We give a necessary and sufficient condition weaker than the homogeneity of symmetric HH-C-orthogonalities which characterizes inner product spaces among normed linear spaces of dimension at least three. In conclusion, some more characterizations of real inner product spaces are provided.
DOI : 10.2298/FIL2214655D
Classification : 46B20, 46C05
Keywords: Carlsson’s orthogonality, Hermite-Hadamard type of unitary Carlsson’s orthogonality, homogeneity of HH-C- orthogonality, inner product space, isosceles orthogonality, Pythagorean orthogonality 
Mahdi Dehghani. Characterization of inner product spaces by unitary Carlsson type orthogonalities. Filomat, Tome 36 (2022) no. 14, p. 4655 . doi: 10.2298/FIL2214655D
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     author = {Mahdi Dehghani},
     title = {Characterization of inner product spaces by unitary {Carlsson} type orthogonalities},
     journal = {Filomat},
     pages = {4655 },
     year = {2022},
     volume = {36},
     number = {14},
     doi = {10.2298/FIL2214655D},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2214655D/}
}
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