PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1999 | 137 | 1 | 61-79
Tytuł artykułu

Geometry of oblique projections

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let A be a unital C*-algebra. Denote by P the space of selfadjoint projections of A. We study the relationship between P and the spaces of projections $P_a$ determined by the different involutions $#_a$ induced by positive invertible elements a ∈ A. The maps $φ:P → P_a$ sending p to the unique $q ∈ P_a$ with the same range as p and $Ω_a : P_a → P_a$ sending q to the unitary part of the polar decomposition of the symmetry 2q-1 are shown to be diffeomorphisms. We characterize the pairs of idempotents q,r ∈ A with ||q-r|| < 1 such that there exists a positive element a ∈ A satisfying $q,r ∈ P_a$. In this case q and r can be joined by a unique short geodesic along the space of idempotents Q of A.
Słowa kluczowe
Twórcy
autor
  • Instituto de Ciencias, Univ. Nac de Gral. Sarmiento, Roca 850, (1663) San Miguel, Pcia. de Buenos Aires, Argentina, eandruch@percanta.ungs.edu.ar
  • Instituto Argentino de Matemática, Saavedra 15 3er piso,(1083) Buenos Aires, Argentina, gcorach@mate.dm.uba.ar
autor
Bibliografia
  • [1] Afriat S. N., Orthogonal and oblique projections and the characteristics of pairs of vector spaces, Proc. Cambridge Philos. Soc. 53 (1957), 800-816.
  • [2] Andruchow E., Corach G. and Stojanoff D., Projective spaces for C*-algebras, Integral Equations Operator Theory, to appear.
  • [3] Brown L. G., The rectifiable metric on the set of closed subspaces of Hilbert space, Trans. Amer. Math. Soc. 337 (1993), 279-289.
  • [4] Buckholtz D., Inverting the difference of Hilbert space projections, Amer. Math. Monthly 104 (1997), 60-61.
  • [5] Coifman R. R., and Murray M. A. M., Uniform analyticity of orthogonal projections, Trans. Amer. Math. Soc. 312 (1989), 779-817.
  • [6] Corach G., Operator inequalities, geodesics and interpolation, in: Functional Analysis and Operator Theory, Banach Center Publ. 30, Inst. Math., Polish Acad. Sci., Warszawa, 1994, 101-115.
  • [7] Corach G., Porta H. and Recht L., Differential geometry of systems of projections in Banach algebras, Pacific J. Math. 140 (1990), 209-228.
  • [8] Corach G., Porta H. and Recht L., Differential geometry of systems of projections in Banach algebras, The geometry of spaces of projections in C*-algebras, Adv. Math. 101 (1993), 59-77.
  • [9] Corach G., Porta H. and Recht L., The geometry of spaces of selfadjoint invertible elements of a C*-algebra, Integral Equations Operator Theory 16 (1993), 771-794.
  • [10] Dieudonné J., Quasi-hermitian operators, in: Proc. Internat. Sympos. Linear Spaces (Jerusalem, 1960), Pergamon Press, Oxford, 1961, 115-122.
  • [11] Gerisch W., Idempotents, their Hermitian components, and subspaces in position p of a Hilbert space, Math. Nachr. 115 (1984), 283-303.
  • [12] Householder A. S., and Carpenter J. A., The singular values of involutory and of idempotent matrices, Numer. Math. 5 (1963), 234-237.
  • [13] Kerzman N., and Stein E. M., The Szegő kernel in terms of Cauchy-Fantappiè kernels, Duke Math. J. 45 (1978), 197-224.
  • [14] Kerzman N., and Stein E. M., The Szegő kernel in terms of Cauchy-Fantappiè kernels, The Cauchy kernel, the Szegő kernel, and the Riemann mapping function, Math. Ann. 236 (1978), 85-93.
  • [15] Kovarik Z. V., Similarity and interpolation between projectors, Acta Sci. Math. (Szeged) 39 (1977), 341-351.
  • [16] Lax P. D., Symmetrizable linear transformations, Comm. Pure Appl. Math. 7 (1954), 633-647.
  • [17] Mizel V. J., and Rao M. M., Nonsymmetric projections in Hilbert space, Pacific J. Math. 12 (1962), 343-357.
  • [18] Odzijewicz A., On reproducing kernels and quantization of states, Comm. Math. Phys. 114 (1988), 577-597.
  • [29] Odzijewicz A., On reproducing kernels and quantization of states, Coherent states and geometric quantization, ibid. 150 (1992), 385-413.
  • [20] Pasternak-Winiarski Z., On the dependence of the orthogonal projector on deformations of the scalar product, Studia Math. 128 (1998), 1-17.
  • [21] Pasternak-Winiarski Z., On the dependence of the orthogonal projector on deformations of the scalar product, On the dependence of the reproducing kernel on the weight of integration, J. Funct. Anal. 94 (1990), 110-134.
  • [22] Pasternak-Winiarski Z., Bergman spaces and kernels for holomorphic vector bundles, Demonstratio Math. 30 (1997), 199-214.
  • [23] Phillips N. C., The rectifiable metric on the space of projections in a C*-algebra, Internat. J. Math. 3 (1992), 679-698.
  • [24] Porta H., and Recht L., Spaces of projections in Banach algebras, Acta Cient. Venezolana 39 (1987), 408-426.
  • [25] Porta H., and Recht L., Spaces of projections in Banach algebras, Minimality of geodesics in Grassmann manifolds, Proc. Amer. Math. Soc. 100 (1987), 464-466.
  • [26] Porta H., and Recht L., Spaces of projections in Banach algebras, Variational and convexity properties of families of involutions, Integral Equations Operator Theory 21 (1995), 243-253.
  • [27] Pták V., Extremal operators and oblique projections, Časopis Pěst. Mat. 110 (1985), 343-350.
  • [28] Strătilă Ş., Modular Theory in Operator Algebras, Editura Academiei, Bucharest, 1981.
  • [29] Zemánek J., Idempotents in Banach algebras, Bull. London Math. Soc. 11 (1979), 177-183.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv137i1p61bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.