# On a property of weak resolvents and its application to a spectral problem

Annales Polonici Mathematici (1997)

- Volume: 66, Issue: 1, page 263-268
- ISSN: 0066-2216

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topYoichi Uetake. "On a property of weak resolvents and its application to a spectral problem." Annales Polonici Mathematici 66.1 (1997): 263-268. <http://eudml.org/doc/269991>.

@article{YoichiUetake1997,

abstract = {We show that the poles of a resolvent coincide with the poles of its weak resolvent up to their orders, for operators on Hilbert space which have some cyclic properties. Using this, we show that a theorem similar to the Mlak theorem holds under milder conditions, if a given operator and its adjoint have cyclic vectors.},

author = {Yoichi Uetake},

journal = {Annales Polonici Mathematici},

keywords = {weak resolvent; cyclic vector; spectral radius; Hardy class; operator model theory; scattering theory; control theory; poles of a resolvent; Mlak theorem; cyclic vectors},

language = {eng},

number = {1},

pages = {263-268},

title = {On a property of weak resolvents and its application to a spectral problem},

url = {http://eudml.org/doc/269991},

volume = {66},

year = {1997},

}

TY - JOUR

AU - Yoichi Uetake

TI - On a property of weak resolvents and its application to a spectral problem

JO - Annales Polonici Mathematici

PY - 1997

VL - 66

IS - 1

SP - 263

EP - 268

AB - We show that the poles of a resolvent coincide with the poles of its weak resolvent up to their orders, for operators on Hilbert space which have some cyclic properties. Using this, we show that a theorem similar to the Mlak theorem holds under milder conditions, if a given operator and its adjoint have cyclic vectors.

LA - eng

KW - weak resolvent; cyclic vector; spectral radius; Hardy class; operator model theory; scattering theory; control theory; poles of a resolvent; Mlak theorem; cyclic vectors

UR - http://eudml.org/doc/269991

ER -

## References

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