# Fractional Powers of Almost Non-Negative Operators

Martínez, Celso; Sanz, Miguel; Redondo, Antonia

Fractional Calculus and Applied Analysis (2005)

- Volume: 8, Issue: 2, page 201-230
- ISSN: 1311-0454

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topMartínez, Celso, Sanz, Miguel, and Redondo, Antonia. "Fractional Powers of Almost Non-Negative Operators." Fractional Calculus and Applied Analysis 8.2 (2005): 201-230. <http://eudml.org/doc/11289>.

@article{Martínez2005,

abstract = {Mathematics Subject Classification: Primary 47A60, 47D06.In this paper, we extend the theory of complex powers of operators to a
class of operators in Banach spaces whose spectrum lies in C ]−∞, 0[ and
whose resolvent satisfies an estimate ||(λ + A)(−1)|| ≤ (λ(−1) + λm)
M for all λ > 0 and for some constants M > 0 and m ∈ R. This class of operators
strictly contains the class of the non negative operators and the one of
operators with polynomially bounded resolvent. We also prove that this
theory may be extended to sequentially complete locally convex spaces.* Work partially supported by Ministerio de Ciencia y Tecnología, Grant BFM2000-1427 and by Generalitat Valenciana, Grant CTIDIB2002-274.},

author = {Martínez, Celso, Sanz, Miguel, Redondo, Antonia},

journal = {Fractional Calculus and Applied Analysis},

keywords = {47A60; 47D06},

language = {eng},

number = {2},

pages = {201-230},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Fractional Powers of Almost Non-Negative Operators},

url = {http://eudml.org/doc/11289},

volume = {8},

year = {2005},

}

TY - JOUR

AU - Martínez, Celso

AU - Sanz, Miguel

AU - Redondo, Antonia

TI - Fractional Powers of Almost Non-Negative Operators

JO - Fractional Calculus and Applied Analysis

PY - 2005

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 8

IS - 2

SP - 201

EP - 230

AB - Mathematics Subject Classification: Primary 47A60, 47D06.In this paper, we extend the theory of complex powers of operators to a
class of operators in Banach spaces whose spectrum lies in C ]−∞, 0[ and
whose resolvent satisfies an estimate ||(λ + A)(−1)|| ≤ (λ(−1) + λm)
M for all λ > 0 and for some constants M > 0 and m ∈ R. This class of operators
strictly contains the class of the non negative operators and the one of
operators with polynomially bounded resolvent. We also prove that this
theory may be extended to sequentially complete locally convex spaces.* Work partially supported by Ministerio de Ciencia y Tecnología, Grant BFM2000-1427 and by Generalitat Valenciana, Grant CTIDIB2002-274.

LA - eng

KW - 47A60; 47D06

UR - http://eudml.org/doc/11289

ER -

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