Geometric significance of Toeplitz kernels
Let L2 be the Lebesgue space of square-integrable functions on the unit circle. We show that the injectivity problem for Toeplitz operators is linked to the existence of geodesics in the Grassmann manifold of L2. We also investigate this connection in the context of restricted Grassmann manifolds as...
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Academic Press Inc.
2018
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| LEADER | 08738caa a22008537a 4500 | ||
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| 001 | PAPER-16857 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518204754.0 | ||
| 008 | 190410s2018 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-85042852654 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 030 | |a JFUAA | ||
| 100 | 1 | |a Andruchow, E. | |
| 245 | 1 | 0 | |a Geometric significance of Toeplitz kernels |
| 260 | |b Academic Press Inc. |c 2018 | ||
| 270 | 1 | 0 | |m Larotonda, G.; Instituto Argentino de Matemática, ‘Alberto P. Calderón’, CONICET, Saavedra 15 3er. piso, Argentina; email: glaroton@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Andruchow, E., Operators which are the difference of two projections (2014) J. Math. Anal. Appl., 420 (2), pp. 1634-1653 | ||
| 504 | |a Andruchow, E., The Grassmann manifold of a Hilbert space (2014) Proceedings of the XIIth Dr. Antonio A.R. Monteiro Congress, pp. 41-55. , Univ. Nac. Sur Dep. Mat. Inst. Mat. Bahía Blanca | ||
| 504 | |a Andruchow, E., Larotonda, G., Hopf–Rinow theorem in the Sato Grassmannian (2008) J. Funct. Anal., 255 (7), pp. 1692-1712 | ||
| 504 | |a Andruchow, E., Larotonda, G., Lagrangian Grassmannian in infinite dimension (2009) J. Geom. Phys., 59 (3), pp. 306-320 | ||
| 504 | |a Andruchow, E., Chiumiento, E., Di Iorio y Lucero, M.E., Essentially commuting projections (2015) J. Funct. Anal., 268 (2), pp. 336-362 | ||
| 504 | |a Antezana, J., Larotonda, G., Varela, A., Optimal paths for symmetric actions in the unitary group (2014) Comm. Math. Phys., 328 (2), pp. 481-497 | ||
| 504 | |a Beltiţă, D., Ratiu, T.S., Tumpach, A.B., The restricted Grassmannian, Banach Lie–Poisson spaces, and coadjoint orbits (2007) J. Funct. Anal., 247 (1), pp. 138-168 | ||
| 504 | |a Böttcher, A., Silbermann, B., Analysis of Toeplitz Operators (1990), Springer-Verlag Berlin; Böttcher, A., Karlovich, A., Silbermann, B., Generalized Krein algebras and asymptotics of Toeplitz determinants (2007) Methods Funct. Anal. Topology, 13 (3), pp. 236-261 | ||
| 504 | |a Bourgain, J., Kozma, G., One cannot hear the winding number (2007) J. Eur. Math. Soc. (JEMS), 9 (4), pp. 637-658 | ||
| 504 | |a Carey, A.L., Some homogeneous spaces and representations of the Hilbert Lie group U(H)2 (1985) Rev. Roumaine Math. Pures Appl., 30 (7), pp. 505-520 | ||
| 504 | |a Clark, D.N., On the point spectrum of a Toeplitz operator (1967) Trans. Amer. Math. Soc., 126, pp. 251-266 | ||
| 504 | |a Corach, G., Porta, H., Recht, L., The geometry of spaces of projections in C⁎-algebras (1993) Adv. Math., 101 (1), pp. 59-77 | ||
| 504 | |a Davis, C., Separation of two linear subspaces (1958) Acta Sci. Math. (Szeged), 19, pp. 172-187 | ||
| 504 | |a Dixmier, J., Position relative de deux veriétés linéaires fermées dans un espace de Hilbert (1948) Rev. Sci., 86, pp. 387-399. , (in French) | ||
| 504 | |a Douglas, R.G., Banach Algebra Techniques in Operator Theory (1998) Graduate Texts in Mathematics, 179. , second edition Springer-Verlag New York | ||
| 504 | |a Goliński, T., Odzijewicz, A., Hierarchy of Hamilton equations on Banach Lie–Poisson spaces related to restricted Grassmannian (2010) J. Funct. Anal., 258 (10), pp. 3266-3294 | ||
| 504 | |a Halmos, P.R., Two subspaces (1969) Trans. Amer. Math. Soc., 144, pp. 381-389 | ||
| 504 | |a Hartmann, A., Mitkovski, M., Kernels of Toeplitz Operators (2016) Contemp. Math., 679. , Amer. Math. Soc. Providence, RI | ||
| 504 | |a Hruščhev, S.V., Nikol'skiı̌, N.K., Pavlov, B.S., Unconditional basis of exponentials and of reproducing kernels (1981) Lecture Notes in Math., 864, pp. 214-335 | ||
| 504 | |a Kovarik, Z.V., Manifolds of linear involutions (1979) Linear Algebra Appl., 24, pp. 271-287 | ||
| 504 | |a Lee, M., Sarason, D., The spectra of some Toeplitz operators (1971) J. Math. Anal. Appl., 33, pp. 529-543 | ||
| 504 | |a Makarov, N., Poltoratski, A., Meromorphic inner functions, Toeplitz kernels and the uncertainty principle (2005) Perspectives in Analysis, Math. Phys. Stud., 27, pp. 185-252. , Springer Berlin | ||
| 504 | |a Makarov, N., Poltoratski, A., Beurling–Malliavin theory for Toeplitz kernels (2010) Invent. Math., 180, pp. 443-480 | ||
| 504 | |a Mitkovski, M., Poltoratski, A., Pólya sequences, Toeplitz kernels and gap theorems (2010) Adv. Math., 224, pp. 1057-1070 | ||
| 504 | |a Nikol'skiı̌, N.K., Treatise on the Shift Operator. Spectral Function Theory (1986) Grundlehren der Mathematischen Wissenschaften, 273. , Springer-Verlag Berlin | ||
| 504 | |a Nikol'skiı̌, N.K., Operators, Functions And Systems: An Easy Reading. Vol. 1. Hardy, Hankel, and Toeplitz (2002) Mathematical Surveys and Monographs, 92. , American Mathematical Society Providence, RI Translated from the French by Andreas Hartmann | ||
| 504 | |a Pavlović, M., Introduction to Function Spaces on the Disk (2004) Posebna Izdanja [Special Editions], 20. , Matematički Institut SANU Belgrade | ||
| 504 | |a Porta, H., Recht, L., Minimality of geodesics in Grassmann manifolds (1987) Proc. Amer. Math. Soc., 100, pp. 464-466 | ||
| 504 | |a Pressley, A., Segal, G., Loop Groups (1986) Oxford Mathematical Monographs, , Oxford Science Publications. The Clarendon Press, Oxford University Press New York | ||
| 504 | |a Sarason, D., Algebras of functions on the unit circle (1973) Bull. Amer. Math. Soc., 79 (2), pp. 286-299 | ||
| 504 | |a Segal, G., Wilson, G., Loop groups and equations of KdV type (1985) Publ. Math. Inst. Hautes Études Sci., 61, pp. 5-65 | ||
| 504 | |a Segal, G., Wilson, G., Loop groups and equations of KdV type (1998) Surveys in Differential Geometry: Integral Systems [Integrable Systems], Surv. Differ. Geom., IV, pp. 403-466. , Int. Press Boston, MA | ||
| 504 | |a Seidel, W., On the distribution of values of bounded analytic functions (1934) Trans. Amer. Math. Soc., 36, pp. 201-226 | ||
| 504 | |a Tumpach, A.B., Hyperkhäler structures and infinite-dimensional Grassmannians (2007) J. Funct. Anal., 243 (1), pp. 158-206 | ||
| 504 | |a Zygmund, A., Trigonometric Series. Vol. I, II (2002) Cambridge Mathematical Library, , third edition Cambridge University Press Cambridge With a foreword by Robert A. Fefferman | ||
| 520 | 3 | |a Let L2 be the Lebesgue space of square-integrable functions on the unit circle. We show that the injectivity problem for Toeplitz operators is linked to the existence of geodesics in the Grassmann manifold of L2. We also investigate this connection in the context of restricted Grassmann manifolds associated to p-Schatten ideals and essentially commuting projections. © 2018 Elsevier Inc. |l eng | |
| 536 | |a Detalles de la financiación: Agencia Nacional de Promoción Científica y Tecnológica, 2010 2478 | ||
| 536 | |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas, PIP 2016 112201 | ||
| 536 | |a Detalles de la financiación: This research was supported by CONICET ( PIP 2016 112201 ) and ANPCyT ( 2010 2478 ). We would like to thank Daniel Suárez for his helpful insight on Toeplitz operators, and the anonymous referee for her/his valuable suggestions to improve this manuscript. | ||
| 593 | |a Instituto de Ciencias, Universidad Nacional de Gral. Sarmiento, J.M. Gutierrez 1150, Los Polvorines, 1613, Argentina | ||
| 593 | |a Departamento de Matemática, Facultad de Ciencias Exactas, Universidad de La Plata, Calles 50 y 115, La Plata, 1900, Argentina | ||
| 593 | |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria (1428) CABA, Argentina | ||
| 593 | |a Instituto Argentino de Matemática, ‘Alberto P. Calderón’, CONICET, Saavedra 15 3er. piso, Buenos Aires, 1083, Argentina | ||
| 690 | 1 | 0 | |a GEODESIC |
| 690 | 1 | 0 | |a SATO GRASSMANNIAN |
| 690 | 1 | 0 | |a SCHATTEN IDEAL |
| 690 | 1 | 0 | |a TOEPLITZ OPERATOR |
| 700 | 1 | |a Chiumiento, E. | |
| 700 | 1 | |a Larotonda, G. | |
| 773 | 0 | |d Academic Press Inc., 2018 |g v. 275 |h pp. 329-355 |k n. 2 |p J. Funct. Anal. |x 00221236 |w (AR-BaUEN)CENRE-287 |t Journal of Functional Analysis | |
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