Bilinear mappings – selected properties and problems

Balcerzak, Marek; Strobin, Filip; Wachowicz, Artur

dc.contributor.author	Balcerzak, Marek
dc.contributor.author	Strobin, Filip
dc.contributor.author	Wachowicz, Artur
dc.contributor.editor	Filipczak, Małgorzata
dc.contributor.editor	Wagner-Bojakowska, Elżbieta
dc.date.accessioned	2019-05-28T10:01:36Z
dc.date.available	2019-05-28T10:01:36Z
dc.date.issued	2013
dc.identifier.citation	Balcerzak M., Strobin F., Wachowicz A., Bilinear mappings – selected properties and problems, [w:] Traditional and present-day topics in real analysis. Dedicated to Professor Jan Stanisław Lipiński, Filipczak M., Wagner-Bojakowska E. (red.), Wydawnictwo Uniwersytetu Łódzkiego, Łódź 2013, s. 281-305, doi: 10.18778/7525-971-1.18	pl_PL
dc.identifier.isbn	978-83-7525-971-1
dc.identifier.uri	http://hdl.handle.net/11089/28703
dc.description.sponsorship	Udostępnienie publikacji Wydawnictwa Uniwersytetu Łódzkiego finansowane w ramach projektu „Doskonałość naukowa kluczem do doskonałości kształcenia”. Projekt realizowany jest ze środków Europejskiego Funduszu Społecznego w ramach Programu Operacyjnego Wiedza Edukacja Rozwój; nr umowy: POWER.03.05.00-00-Z092/17-00.	pl_PL
dc.language.iso	en	pl_PL
dc.publisher	Wydawnictwo Uniwersytetu Łódzkiego	pl_PL
dc.relation.ispartof	Filipczak M., Wagner-Bojakowska E. (red.), Traditional and present-day topics in real analysis. Dedicated to Professor Jan Stanisław Lipiński, Wydawnictwo Uniwersytetu Łódzkiego, Łódź 2013;
dc.rights	Attribution-NonCommercial-NoDerivatives 4.0 Międzynarodowe	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/	*
dc.subject	bilinear mapping	pl_PL
dc.subject	multiplication	pl_PL
dc.subject	convolution	pl_PL
dc.subject	Banach spaces	pl_PL
dc.subject	open mapping	pl_PL
dc.subject	meagerness	pl_PL
dc.subject	porosity	pl_PL
dc.title	Bilinear mappings – selected properties and problems	pl_PL
dc.type	Book chapter	pl_PL
dc.page.number	281-305	pl_PL
dc.contributor.authorAffiliation	Łódź University of Technology, Institute of Mathematics	pl_PL
dc.references	F. Abtahi, R. Nasr–Isfahani, A. Rejali, On the Lp–conjecture for locally compact groups, Arch. Math. (Basel) 89 (2007), 237–242.	pl_PL
dc.references	C. R. Adams, The space of functions of bounded variation and certain general spaces, Trans. Amer. Math. Soc. 40 (1936), 421–438.	pl_PL
dc.references	C. R. Adams, J. A. Clarkson, On convergence in variation, Bull. Amer. Math. Soc. 40 (1934), 413–417.	pl_PL
dc.references	C. R. Adams, A. P. Morse, On the space (BV), Trans. Amer. Math. Soc. 42 (1937), 194–205.	pl_PL
dc.references	I. Akbarbaglu, S. Maghsoudi, An answer to a question on the convolution of functions, Arch. Math. (Basel) 98 (2012), 545–553.	pl_PL
dc.references	I. Akbarbaglu, S. Maghsoudi, Porosity and products of Orlicz spaces, Positivity, to appear, DOI: 10.1007/s11117-012-0218-0	pl_PL
dc.references	I. Akbarbaglu, S. Maghsoudi, Porosity of certain subsets of Lebesgue spaces on locally compact groups, Bull. Austral. Math. Soc., to appear, DOI:10.1017/S0004972712000949.	pl_PL
dc.references	M. Balcerzak, A. Majchrzycki, A. Wachowicz, Openness of multiplication in some function spaces, Taiwanese J. Math. 17 (2013), 1115–1126.	pl_PL
dc.references	M. Balcerzak, A. Majchrzycki, F. Strobin, Uniform openness of multiplication in Banach spaces Lp, preprint available at: http://arxiv.org/abs/1309.3433.	pl_PL
dc.references	M. Balcerzak, A. Maliszewski, On multiplication in spaces of continuous functions, Colloq. Math. 122 (2011), 247–253.	pl_PL
dc.references	M. Balcerzak, A.Wachowicz, Some examples of meager sets in Banach spaces, Real Anal. Exchange 26 (2000/01), 877–884.	pl_PL
dc.references	M. Balcerzak, A. Wachowicz, W. Wilczyński, Multiplying balls in C[0;1], Studia Math. 170 (2005), 203–209.	pl_PL
dc.references	E. Behrends, Walk the dog, or: products of open balls in the space of continuous functions, Func. Approx. Comment. Math. 44 (2011), 153–164.	pl_PL
dc.references	E. Behrends, Products of n open subsets in the space of continuous functions on [0;1], Studia Math. 204 (2011), 73–95.	pl_PL
dc.references	M. Burke, Continuous functions which take a somewhere dense set of values on every open set, Topology Appl. 103 (2000), 95–110.	pl_PL
dc.references	V. V. Chistyakov, unpublished notes, 2011.	pl_PL
dc.references	P. J. Cohen, A counterexample to the closed graph theorem for bilinear maps, J. Funct. Anal. 16 (1974), 235–239.	pl_PL
dc.references	P. G. Dixon, Generalized open mapping theorems for bilinear maps, with an application to operator algebras, Proc. Amer. Math. Soc. 104 (1988), 106–110.	pl_PL
dc.references	R. Engelking, General topology, second edition, Sigma Series in Pure Mathematics 6. Heldermann Verlag, Berlin, 1989.	pl_PL
dc.references	M. Fabian, P. Hájek, V. Montesinos Santalucia, J. Pelant, V. Zizler, Functional Analysis and Infinite-Dimensional Geometry, CMS Books in Mathematics, Springer, New York, 2001.	pl_PL
dc.references	L. Grafakos, Classical Fourier Analysis, second edition, Graduate Texts in Mathematics 249 Springer, New York, 2008.	pl_PL
dc.references	S. Głąb, F. Strobin, Dichotomies for Lp spaces, J. Math. Anal. Appl. 368 (2010), 382–390.	pl_PL
dc.references	S. Głąb, F. Strobin, Dichotomies for C0(X) and Cb(X) spaces, Czechoslovak Math. J. 63 (2013), 91-105.	pl_PL
dc.references	S. Głąb, F. Strobin, Porosity and the Lp-conjecture, Arch. Math. (Basel) 95 (2010), 583-592.	pl_PL
dc.references	S. Głąb, ChanWoo Yang, F. Strobin, Dichotomies for Lorentz spaces, Central European J. Math. 11 (2013), 1228–1242.	pl_PL
dc.references	P. Halmos, Measure Theory, D. Van Nostrand Company, Inc., New York, 1950.	pl_PL
dc.references	C. Horowitz, An elementary counterexample to the open mapping principle for bilinear maps, Proc. Amer. Math. Soc. 53 (1975), 293–294.	pl_PL
dc.references	J. Jachymski, A nonlinear Banach-Steinhaus theorem and some meager sets in Banach spaces, Studia Math. 170 (2005), 303–320.	pl_PL
dc.references	A. Komisarski, A connection between multiplication in C(X) and the dimension of X, Fund. Math. 189 (2006), 149–154.	pl_PL
dc.references	S. Kowalczyk, Weak openness of multiplication in C(0;1), Real Anal. Exchange 35 (2010), 235–241.	pl_PL
dc.references	S. Kowalczyk, On operations in C(X) determined by continuous functions, Acta Math. Hungar., to appear.	pl_PL
dc.references	R. Kunze, E. Stein, Uniformly bounded representations and harmonic analysis of the 2x2 real unimodular group, Amer. J. Math. 82 (1960), 1–62.	pl_PL
dc.references	Li Ronglu, Zhong Shuhui, C. Swartz, An open mapping theorem without continuity and linearity, Topology Appl. 157 (2010), 2086–2093.	pl_PL
dc.references	V. Olevskii, A note on the Banach-Steinhaus theorem, Real Anal. Exchange 17 (1991/92), 399–401.	pl_PL
dc.references	T. Quek, L. Yap, Sharpness of Young’s inequality for convolution, Math. Scand. 53 (1983), 221–237.	pl_PL
dc.references	N. Rickert, Convolution of Lp functions, Proc. Amer. Math. Soc., 18 (1967), 762– 763.	pl_PL
dc.references	W. Rudin, Functional Analysis, second edition, McGraw-Hill Inc. 1991.	pl_PL
dc.references	S. Saeki, The Lp–conjecture and Young’s inequality, Illinois. J. Math. 34 (1990), 615–627.	pl_PL
dc.references	S.M. Srivastava, A Course on Borel Sets, Springer, New York, 1998.	pl_PL
dc.references	F. Strobin, The porosity of convex nowhere dense subsets of normed linear spaces, Abstr. Appl. Anal. (2009), Article ID 243604, 11 pp.	pl_PL
dc.references	F. Strobin, Dichotomies for Orlicz spaces, accepted in Mathematica Slovaca.	pl_PL
dc.references	F. Strobin, Genericity and porosity of some subsets of function spaces, PhD thesis, Institute of Mathematics of the Polish Academy of Sciences, 2011, available at: http://im0.p.lodz.pl/˜filip	pl_PL
dc.references	A.Wachowicz, Multiplying balls in C(n)[0;1], Real Anal. Exchange 34 (2009), 445– 450.	pl_PL
dc.references	A. Wachowicz, On some residual subsets, PhD thesis, Łódź University of Technology, 2004 (in Polish).	pl_PL
dc.references	L. Zajíček, Porosity and σ-porosity, Real Anal. Exchange 13 (1987/88), 314–350.	pl_PL
dc.references	L. Zajíček, On σ-porous sets in abstract spaces, Abstr. Appl. Anal. 5 (2005), 509– 534.	pl_PL
dc.contributor.authorEmail	marek.balcerzak@p.lodz.pl	pl_PL
dc.contributor.authorEmail	filip.strobin@p.lodz.pl	pl_PL
dc.contributor.authorEmail	artur.wachowicz@p.lodz.pl	pl_PL
dc.identifier.doi	10.18778/7525-971-1.18
dc.subject.msc	46B25
dc.subject.msc	47A06
dc.subject.msc	54C10