Interpolated subspaces of exponential vectors of the unbounded operators in Banach spaces

• Autorzy: Dmytryshyn M. , Lopushansky O.
• Języki publikacji: EN

Abstrakty

EN

It is shown that the spectral subspaces of the unbounded operators in Ba-nach spaces and also their integer degrees can be described with help of interpolation. The spectral subspaces of operators are described on the basis of abstract Bernstein inequality. The results are applied to research of the root subspaces of regular elliptic operators in a bounded domains.

Słowa kluczowe

EN

exponential vectors; interpolation; spectral theory

PL

interpolacja

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2004
• Tom: Vol. 37, nr 1
• Strony: 149--158
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Dmytryshyn M.

• Institute for Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, 3b Naukova, St. 79053 Lviv, Ukraine

autor

Lopushansky O.

• Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland

Bibliografia

• [1] A. Bednarz, O. Lopushansky, Exponential type vectors of isometric group generators, Matem. Studii 18 (1) (2002), 99-106.
• [2] J. Bergh, J. Löfström, Interpolation Spaces, Springer, Berlin-Heidelberg-New York 1976.
• [3] N . Dunford, J.T. Schwartz, Linear Operators, I. Intersci. Publ., New York, London 1958.
• [4] M.L. Gorbachuk , V.I. Gorbachuk, On approximation of smooth vectors of closed operator by entire exponential type vectors, Ukrain. Math. J. 47(5) (1995), 616-628 (in Ukrainian).
• [5] V. Gorbachuk, A. Knyazyuk, The boundary value of solutions of differential-operators equations, Uspehi Matem. Nauk 44(3) (1989), 55-91 (in Russian).
• [6] Ju.I. Ljubič, V.I. Macaev, On operators with a separable spectrum, Amer. Math. Soc. Transl. 47(2) (1965), 89-129.
• [7] O. Lopushansky, M. Dmytryshyn, Vectors of exponential type of operators with discrete spectrum, Matem. Studii. 9(1) (1988) , 70-77.
• [8] O. Lopushansky, M. Dmytryshyn, Operator calculus on the exponential type vectors of the operator with point spectrum, in: General Topology in Banach Spaces, Nova Sci. Publ., Huntingon, New York, 2001, 137-145.
• [9] Ya. Radyno, The vectors of exponential type in operators calculus and differential equations, Differential Equations 21 (9) (1985), 1559-1569 (in Russian).
• [10] G. Radzievskii, The direct and invert theorems in approximation problems by finite degree vectors, Matem. Sbornik 189(4) (1988), 83-124 (in Russian) .
• [11] H. Triebel, Interpolation Theory. Function Spaces. Differential Operators, Springer, Berlin-Heidelberg-New York 1995.