On solvability of nonlinear operator equations and eigenvalues of homogeneous operators

Věra Burýšková; Slavomír Burýšek

Mathematica Bohemica (1996)

  • Volume: 121, Issue: 3, page 301-314
  • ISSN: 0862-7959

Abstract

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Notions as the numerical range W ( S , T ) and the spectrum ( S , T ) of couple ( S , T ) of homogeneous operators on a Banach space are used to derive theorems on solvability of the equation S x - l T x = y . Conditions for the existence of eigenvalues of the couple ( S , T ) are given.

How to cite

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Burýšková, Věra, and Burýšek, Slavomír. "On solvability of nonlinear operator equations and eigenvalues of homogeneous operators." Mathematica Bohemica 121.3 (1996): 301-314. <http://eudml.org/doc/247946>.

@article{Burýšková1996,
abstract = {Notions as the numerical range $W(S,T)$ and the spectrum $(S,T)$ of couple $(S,T)$ of homogeneous operators on a Banach space are used to derive theorems on solvability of the equation $Sx-lTx=y.$ Conditions for the existence of eigenvalues of the couple $(S,T)$ are given.},
author = {Burýšková, Věra, Burýšek, Slavomír},
journal = {Mathematica Bohemica},
keywords = {Banach and Hilbert space; homogeneous operator; polynomial operator; symmetric operator; monotone operator; numerical range; spectrum; eigenvalue; Banach and Hilbert space; homogeneous operator; polynomial operator; symmetric operator; monotone operator; numerical range; spectrum; eigenvalue},
language = {eng},
number = {3},
pages = {301-314},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On solvability of nonlinear operator equations and eigenvalues of homogeneous operators},
url = {http://eudml.org/doc/247946},
volume = {121},
year = {1996},
}

TY - JOUR
AU - Burýšková, Věra
AU - Burýšek, Slavomír
TI - On solvability of nonlinear operator equations and eigenvalues of homogeneous operators
JO - Mathematica Bohemica
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 121
IS - 3
SP - 301
EP - 314
AB - Notions as the numerical range $W(S,T)$ and the spectrum $(S,T)$ of couple $(S,T)$ of homogeneous operators on a Banach space are used to derive theorems on solvability of the equation $Sx-lTx=y.$ Conditions for the existence of eigenvalues of the couple $(S,T)$ are given.
LA - eng
KW - Banach and Hilbert space; homogeneous operator; polynomial operator; symmetric operator; monotone operator; numerical range; spectrum; eigenvalue; Banach and Hilbert space; homogeneous operator; polynomial operator; symmetric operator; monotone operator; numerical range; spectrum; eigenvalue
UR - http://eudml.org/doc/247946
ER -

References

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