Abstract
Certain characterizations of the Friedrichs and the Kre\(\breve{\imath }\)n von-Neumann extensions of the tensor product of two nonnegative linear relations A and B in terms of the Friedrichs and the Kre\(\breve{\imath }\)n-von Neumann extensions of A and B are provided. A characterization of the extremal extensions of the tensor product of A and B is also given.
Similar content being viewed by others
References
Arlinski\(\breve{\imath }\), Y.M., Hassi, S., Sebestyén, Z., de Snoo, H.S.V.:On the class of extremal extensions of a nonnegative operator, Oper. Theory: Adv. Appl. (B. Sz.-Nagy memorial volume), 127, 41–81 (2001)
Arlinski\(\breve{\imath }\), Y.M., Tsekanovski\(\breve{\imath }\), E.R.: Quasi selfadjoint contractive extensions of Hermitian contractions. Teor. Funkts., Funkts. Anal. Prilozhen, 50, 9–16 (1988)
Chryssomalakos, C., Engeldinger, R.A., Jurc̆o, B., Schlieker, M., Zumino, B.: Complex quantum envelo** algebras as twisted tensor products. Lett. Math. Phys. 32(4), 275–281 (1994)
Coddington, E.A., de Snoo, H.S.V.: Positive selfadjoint extensions of positive symmetric subspaces. Math. Z. 159, 203–214 (1978)
Farkas, B., Matolcsi, M.: Commutation properties of the form sum of positive, symmetric operators. Acta Sci. Math. (Szeged) 6, 777–790 (2001)
Hassi, S., de Snoo, H.S.V., Szafraniec, F.H.: Componentwise and Cartesian decompositions of linear relations. Diss. Math. 465, 59 (2009)
Hassi, S., Sandovici, A., de Snoo, H.S.V., Winkler, H.: Form sums of nonnegative selfadjoint operators. Acta Math. Hung. 111, 81–105 (2006)
Hassi, S., Sandovici, A., de Snoo, H.S.V., Winkler, H.: A general factorization approach to the extension theory of nonnegative operators and relations. J. Oper. Theory 58(2), 351–386 (2007)
Hassi, S., Sandovici, A., de Snoo, H.S.V., Winkler, H.: Extremal extensions for the sum of nonnegative selfadjoint relations. Proc. Am. Math. Soc. 135, 3193–3204 (2007)
Jacobs, H., Yoshimura, H.: Tensor products of Dirac structures and interconnection in Lagrangian mechanical systems, ar**v:1105.0105v2 [math.SG]
Kawamura, K.: A tensor product of representations of Cuntz algebras. Lett. Math. Phys. 82(1), 91–104 (2007)
Nafalska, M.M.: Extremal Extensions of the Tensor Product of Nonnegative Operators, PAMM. Proc. Appl. Math. Mech. 9, 659–660 (2009)
Nafalska, M.M.: Extremal extensions of nonnegative operators with applications. Doctoral thesis, Technische Universitat Berlin (2008)
Reed, M., Simon, B.: Methods of Modern Mathematical Physics, I Functional Analisys, Revised and Enlarged Edition. Academic Press Inc., San Diego (1980)
Roman, M., Sandovici, A.: The composition and the tensor product of Dirac structures on infinite–dimensional spaces (in preparation)
Sebestyén, Z., Stochel, J.: Restrictions of positive self-adjoint operators. Acta Sci. Math. (Szeged) 55, 149–154 (1991)
Sebestyén, Z., Stochel, J.: On products of unbounded operators. Acta Math. Hung. 100(1–2), 105–129 (2003)
Weidmann, J.: Linear Operators in Hilbert Spaces. Springer, Berlin (1980)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Roman, M., Sandovici, A. A Factorization Approach to the Extension Theory of the Tensor Product of Nonnegative Linear Relations. Results Math 72, 875–891 (2017). https://doi.org/10.1007/s00025-017-0719-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00025-017-0719-z