Nội suy và các họ $$\mathcal {C}_{0}$$-nửa nhóm không thể mở rộng

Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis. A Hitchhiker’s Guide, 3rd edn. Springer, Berlin (2006)

Andô, T.: On a pair of commutative contractions. Acta Sci. Math. (Szeged) 24, 88–90 (1963)

Bhat, B.R., Skeide, M.: Pure semigroups of isometries on Hilbert $$C^{\ast }$$-modules. J. Funct. Anal. 269, 1539–1562 (2015)

Crabb, M.J., Davie, A.M.: von Neumann’s inequality for Hilbert space operators. Bull. Lond. Math. Soc. 7, 49–50 (1975)

Dahya, R.: On the complete metrisability of spaces of contractive semigroups. Arch. Math. (Basel) 118, 509–528 (2022)

Dahya, R.: The space of contractive $$C_{0}$$-semigroups is a Baire space. J. Math. Anal. Appl. 508, 125881 (2022)

Dahya, R.: Dilations of commuting $$C_{0}$$-semigroups with bounded generators and the von Neumann polynomial inequality. J. Math. Anal. Appl. 523, 127021 (2023)

Dahya, R.: Characterisations of dilations via approximants, expectations, and functional calculi. J. Math. Anal. Appl. 529, 127607 (2024)

Doob, J.L.: Stochastic Processes. Wiley Classics Library, Wiley, New York (1990). Reprint of the 1953 original, A Wiley-Interscience Publication

Dynkin, E.B.: Markov Processes, vol. I. Springer, Berlin (1965)

Eisner, T.: Embedding operators into strongly continuous semigroups. Arch. Math. (Basel) 92, 451–460 (2009)

Eisner, T.: A ‘typical’ contraction is unitary. Enseign. Math. (2) 56, 403–410 (2010)

Eisner, T.: Stability of operators and operator semigroups. Operator Theory: Advances and Applications, vol. 209. Birkhäuser Verlag, Basel (2010)

Eisner, T., Farkas, B., Haase, M., Nagel, R.: Operator theoretic aspects of ergodic theory. Graduate Texts in Mathematics, vol. 272. Springer, Cham (2015)

Eisner, T., Mátrai, T.: On typical properties of Hilbert space operators. Isr. J. Math. 195, 247–281 (2013)

Eisner, T., Radl, A.: Embeddability of real and positive operators. Linear Multilinear Algebra 70, 3747–3767 (2022)

Eisner, T., Serény, A.: Category theorems for stable operators on Hilbert spaces. Acta Sci. Math. (Szeged) 74, 259–270 (2008)

Eisner, T., Serény, A.: Category theorems for stable semigroups. Ergod. Theory Dyn. Syst. 29, 487–494 (2009)

Engel, K.-J., Nagel, R.: One-parameter semigroups for linear evolution equations. Graduate Texts in Mathematics, vol. 194. Springer, New York (2000)

GaŞpar, D., Suciu, N.: On the generalized von Neumann inequality. In: Kérchy, L., Gohberg, I., Foias, C.I., Langer, H. (eds.) Recent Advances in Operator Theory and Related Topics, pp. 291–304. Birkhäuser, Basel (2001)

Grivaux, S., Matheron, É.: Local spectral properties of typical contractions on $$\ell _{p}$$-spaces. Anal. Math. 48, 755–778 (2022)

Grivaux, S., Matheron, É., Menet, Q.: Does a typical $$\ell _{p}$$-space contraction have a non-trivial invariant subspace? Trans. Am. Math. Soc. 374, 7359–7410 (2021)

Grivaux, S., Matheron, É., Menet, Q.: Linear dynamical systems on Hilbert spaces: typical properties and explicit examples. Mem. Am. Math. Soc. 269, pp. v+147 (2021)

Haase, M.: The functional calculus approach to the spectral theorem. Indag. Math. 31, 1066–1098 (2020)

Hille, E., Phillips, R.S.: Functional analysis and semi-groups. American Mathematical Society Colloquium Publications, vol. 31. American Mathematical Society, Providence (1957)

Holbrook, J.A.R., Halmos, P.R.: Spectral dilations and polynomially bounded operators. Indiana Univ. Math. J. 20, 1027–1034 (1971)

Hytönen, T., van Neerven, J., Veraar, M., Weis, L.: Analysis in Banach spaces. Vol. II. Probabilistic Methods and Operator Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 67. 3. Folge. A Series of Modern Surveys in Mathematics. Springer, Cham (2017)

Kadison, R.V., Ringrose, J.R.: Fundamentals of the theory of operator algebras. Vol. I. Pure and Applied Mathematics, vol. 100. Academic Press, Inc. [Harcourt Brace Jovanovich Publishers], New York (1983)

Kechris, A.S.: Classical descriptive set theory. Graduate Texts in Mathematics, vol. 156. Springer, New York (1995)

Klenke, A.: Probability theory, pp. xii+616. Translated from the 2006 German original (2008)

Król, S.: A note on approximation of semigroups of contractions on Hilbert spaces. Semigroup Forum 79, 369–376 (2009)

Murphy, G.J.: C$$^{\ast }$$-algebras and Operator Theory. Academic Press Inc, Boston (1990)

Parrott, S.: Unitary dilations for commuting contractions. Pac. J. Math. 34, 481–490 (1970)

Pedersen, G.K.: Analysis now. Graduate Texts in Mathematics, vol. 118. Springer, New York (1989)

Pedersen, G.K.: C$$^{\ast }$$-algebras and their automorphism groups, Pure and Applied Mathematics (Amsterdam). Academic Press, London (2018)

Peller, V.V.: Estimates of operator polynomials in an $$L^{p}$$ space in terms of the multiplier norm, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 65, 133–148 (1976). Investigations on linear operators and the theory of functions, VII

Peller, V.V.: Estimates of operator polynomials in the space $$L^{p}$$ with respect to the multiplier norm. J. Sov. Math. 16, 1139–1149 (1981)

Ptak, M.: Unitary dilations of multi-parameter semi-groups of operators. Ann. Polon. Math. XLV, 237–243 (1985)

Shalit, O., Skeide, M.: CP-Semigroups and Dilations, Subproduct Systems and Superproduct Systems: The Multi-Parameter Case and Beyond. Preprint available under arXiv:2003.05166 (2022)

Shalit, O.M.: Dilation theory: a guided tour. In: Operator theory, functional analysis and applications, Oper. Theory Adv. Appl., vol. 282, pp. 551–623. Birkhäuser/Springer, Cham (2021)

Słociński, M.: Unitary dilation of two-parameter semi-groups of contractions. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astron. Phys. 22, 1011–1014 (1974)

Słociński, M.: Unitary dilation of two-parameter semi-groups of contractions II. Zeszyty Naukowe Uniwersytetu Jagiellońskiego 23, 191–194 (1982)

Szőkefalvi-Nagy, B.: Sur les contractions de l’espace de Hilbert. Acta Sci. Math. (Szeged) 15, 87–92 (1953)

Szőkefalvi-Nagy, B., FoiaşC.: Harmonic analysis of operators on Hilbert space. North-Holland Publishing Co., Amsterdam; American Elsevier Publishing Co., Inc., New York; Akadémiai Kiadó, Budapest (1970). Translated from the French and revised

Varopoulos, N.T.: Sur une inégalité de von Neumann. C. R. Acad. Sci. Paris Sér. A-B 277, A19–A22 (1973)

Varopoulos, N.T.: On an inequality of von Neumann and an application of the metric theory of tensor products to operators theory. J. Funct. Anal. 16, 83–100 (1974)

Vershik, A.M.: What does a generic Markov operator look like? St. Petersb. Math. J. 17, 763–772 (2006)