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001-es BibID:	BIBFORM081450
Első szerző:	Gehér György Pál (matematikus)
Cím:	Isometries of Grassmann spaces / György Pál Gehér, Peter Semrl
Dátum:	2016
ISSN:	0022-1236
Megjegyzések:	Botelho, Jamison, and Molnár have recently described the general form of surjective isometries of Grassmann spaces on complex Hilbert spaces under certain dimensionality assumptions. In this paper we provide a new approach to this problem which enables us first, to give a shorter proof and second, to remove dimensionality constraints completely. In one of the low dimensional cases, which was not covered by Botelho, Jamison, and Molnár, an exceptional possibility occurs. As a byproduct, we are able to handle the real case as well. Furthermore, in finite dimensions we remove the surjectivity assumption. A variety of tools is used in order to achieve our goal, such as topological, geometrical and linear algebra techniques. The famous two projections theorem for two finite rank projections will be re-proven using linear algebraic methods. A theorem of Györy and the second author on orthogonality preservers on Grassmann spaces will be strengthened as well. This latter result will be obtained by using Chow's fundamental theorem of geometry of Grassmannians.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban folyóiratcikk Isometries Grassmann space Projections Gap metric
Megjelenés:	Journal Of Functional Analysis. - 270 : 4 (2016), p. 1585-1601. -
További szerzők:	Šemrl, Peter
Pályázati támogatás:	OTKA K 115383 OTKA Lendület Program LP2012-46/2012 egyéb
Internet cím:	Szerző által megadott URL DOI Intézményi repozitóriumban (DEA) tárolt változat
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