On polynomial orthogonality on Banach spaces

A.V.Zagorodnyuk

In the paper the notion of orthogonality with respect to a homogeneous polynomial $p$ of arbitrary degree on a Banach space is defined and some properties of $p$-orthogonal sequences are studied. Some application for divisibility of polynomials on Banach spaces are given.

1. Aron R. M., Rueda M. P., A problem concerning zero-subspaces of homogeneous polynomials, Linear Topological Spaces and Complex Analysis, 3 (1997), 20–23.

2. Dineen S., Complex analysis in locally convex spaces, North-Holland Mathematics Studies, 57 (1981).

3. Mazur S., Orlicz W., Sur la divisibilité des polynômes abstraits, C.R. Acad. Sci., Paris, 202 (1936), 621–623.

4. Plichko A., Zagorodnyuk A., On automatic continuity and three problems of “The Scottish Book” concerning the boundedness of polynomial functions, J. Math. Anal. Appl., 220 (1998), 477–494.

5. G. Köthe, Stanislaw Mazur's contributions to functional analysis, Math. Ann. 277 (1987), 489–452.

6. van der Waerden, B. L., Modern Algebra, Ungar (1964).

7. Zagorognyuk A. V., The existence of a linear manifold in a kernel of a complex polynomial functional on a finite dimensional linear space, Matematychni Studii, 8 (1997), no. 1, 115–118. (in Ukrainian)

8. Zagorognyuk A., Groups of symmetry of zero-set of polynomial functionals on complex Banach spaces, Mathematical Methods and Physicomechanical Fields, 41 (1998), no. 3, 20–23. (in Ukrainian)

9. Zagorodnyuk A., On two statements of “The Scottish Book" concerning the ring of bounded polynomial functionals on Banach spaces, Ukrain. Mat. J. 48 (1996), no. 10, 1507–1516.

	On polynomial orthogonality on Banach spaces
Author	A.V.Zagorodnyuk sirand@mebm.lviv.ua Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., L'viv, 290601 Ukraine
Abstract	In the paper the notion of orthogonality with respect to a homogeneous polynomial $p$ of arbitrary degree on a Banach space is defined and some properties of $p$-orthogonal sequences are studied. Some application for divisibility of polynomials on Banach spaces are given.
Keywords	homogeneous polynomials, Banach spaces, p-orthogonal sequences, properties of orthogonal sequences, divisibility of polynomials, functional analysis
DOI	doi:10.30970/ms.14.2.189-192
Reference	1. Aron R. M., Rueda M. P., A problem concerning zero-subspaces of homogeneous polynomials, Linear Topological Spaces and Complex Analysis, 3 (1997), 20–23. 2. Dineen S., Complex analysis in locally convex spaces, North-Holland Mathematics Studies, 57 (1981). 3. Mazur S., Orlicz W., Sur la divisibilité des polynômes abstraits, C.R. Acad. Sci., Paris, 202 (1936), 621–623. 4. Plichko A., Zagorodnyuk A., On automatic continuity and three problems of “The Scottish Book” concerning the boundedness of polynomial functions, J. Math. Anal. Appl., 220 (1998), 477–494. 5. G. Köthe, Stanislaw Mazur's contributions to functional analysis, Math. Ann. 277 (1987), 489–452. 6. van der Waerden, B. L., Modern Algebra, Ungar (1964). 7. Zagorognyuk A. V., The existence of a linear manifold in a kernel of a complex polynomial functional on a finite dimensional linear space, Matematychni Studii, 8 (1997), no. 1, 115–118. (in Ukrainian) 8. Zagorognyuk A., Groups of symmetry of zero-set of polynomial functionals on complex Banach spaces, Mathematical Methods and Physicomechanical Fields, 41 (1998), no. 3, 20–23. (in Ukrainian) 9. Zagorodnyuk A., On two statements of “The Scottish Book" concerning the ring of bounded polynomial functionals on Banach spaces, Ukrain. Mat. J. 48 (1996), no. 10, 1507–1516.
Pages	189-192
Volume	14
Issue	2
Year	2000
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html