A. R. Abdullaev

Steady properties of elements in Banach spaces

In this paper the most general statements concerning steady properties of elements in Banach spaces are stated. The paper provides a device for research of concrete steady properties of linear operators and linear boundary value problems. It is proved that each steady property is generated by some positively homogeneous and nonexpanding functional. The concept of the spectrum of an element concerning steady property is introduced and basic statements about the spectrum are formulated.

Mathematics Subject Classification: 34B05, 34K06, 46B28, 47A10, 47A55, 47L05.

Key words and phrases: Banach spaces, steady properties, generating functional, spaces of linear operators, spectrum, resolvent.