# Interpolation of real method spaces via some ideals of operators

Mieczysław Mastyło; Mario Milman

Studia Mathematica (1999)

- Volume: 136, Issue: 1, page 17-35
- ISSN: 0039-3223

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topMastyło, Mieczysław, and Milman, Mario. "Interpolation of real method spaces via some ideals of operators." Studia Mathematica 136.1 (1999): 17-35. <http://eudml.org/doc/216657>.

@article{Mastyło1999,

abstract = {Certain operator ideals are used to study interpolation of operators between spaces generated by the real method. Using orbital equivalence a new reiteration formula is proved for certain real interpolation spaces generated by ordered pairs of Banach lattices of the form $(X,L_∞(w))$. As an application we extend Ovchinnikov’s interpolation theorem from the context of classical Lions-Peetre spaces to a larger class of real interpolation spaces. A description of certain abstract J-method spaces is also presented.},

author = {Mastyło, Mieczysław, Milman, Mario},

journal = {Studia Mathematica},

keywords = {Lions-Peetre spaces; theorem of Ovchinnikov; -summing operators; abstract real method; quasi-normed lattices; multiplicators; quasi-Banach space; quasi-norm; Banach lattice; factorisation theorem of Graham Bennett},

language = {eng},

number = {1},

pages = {17-35},

title = {Interpolation of real method spaces via some ideals of operators},

url = {http://eudml.org/doc/216657},

volume = {136},

year = {1999},

}

TY - JOUR

AU - Mastyło, Mieczysław

AU - Milman, Mario

TI - Interpolation of real method spaces via some ideals of operators

JO - Studia Mathematica

PY - 1999

VL - 136

IS - 1

SP - 17

EP - 35

AB - Certain operator ideals are used to study interpolation of operators between spaces generated by the real method. Using orbital equivalence a new reiteration formula is proved for certain real interpolation spaces generated by ordered pairs of Banach lattices of the form $(X,L_∞(w))$. As an application we extend Ovchinnikov’s interpolation theorem from the context of classical Lions-Peetre spaces to a larger class of real interpolation spaces. A description of certain abstract J-method spaces is also presented.

LA - eng

KW - Lions-Peetre spaces; theorem of Ovchinnikov; -summing operators; abstract real method; quasi-normed lattices; multiplicators; quasi-Banach space; quasi-norm; Banach lattice; factorisation theorem of Graham Bennett

UR - http://eudml.org/doc/216657

ER -

## References

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- [10] G. Ya. Lozanovskiĭ, On some Banach lattices IV, Sibirsk. Mat. Zh. 14 (1973), 140-155 (in Russian); English transl.: Siberian Math. J. 14 (1973), 97-108.
- [11] L. Maligranda and M. Mastyło, Inclusion mappings between Orlicz sequence spaces, Report No. 090/1998, 12 pp., Faculty of Math. & Comp. Sci., Poznań. Zbl0982.46017
- [12] V. I. Ovchinnikov, The methods of orbits in interpolation theory, Math. Rep. 1 (1984), 349-516.
- [13] V. I. Ovchinnikov, Interpolation theorems for ${L}_{p},q$-spaces, Mat. Sb. 136 (1988), 227-240 (in Russian). Zbl0657.46056
- [14] A. Pietsch, Operator Ideals, North-Holland, Berlin, 1978.
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- [16] G. Sparr, Interpolation of weighted ${L}_{p}$-spaces, ibid. 62 (1978), 229-271. Zbl0393.46029

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