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Hovey and Palmieri [ The structure of the Bousfield lattice , Amer. Math. Soc., Providence, RI, 1999] proposed the retract conjecture on the Bousfield lattice of the stable homotopy category. The author, Shimomura and Tatehara [Publ. Res. Inst. Math. Sci. 50 (2014), pp. 497–513] defined the notion of monoidal posets as a generalization of the Bousfield lattice. In this paper, we prove that an analogue of the retract conjecture holds on a sublattice of monoidal posets. [ABSTRACT FROM AUTHOR]

In this paper a multiplier theorem in the Hardy space H^1(\mathbb {T}) associated with Jacobi expansions of exponential type is proved, that is, a bilateral sequence \left \{\lambda _n\right \}_{n=-\infty }^{\infty } is a multiplier from H^1(\mathbb {T}) into the sequence space \ell ^1(\mathbb {Z}) associated with Jacobi expansions of exponential type, if \[ \sup _N\sum _{k=1}^{\infty }\left (\sum _{kN<|j|\le (k+1)N}|\lambda _j|\right)^2<\infty.\] This is a generalization of a multiplier theorem on usual Fourier expansions in the Hardy space H^1(\mathbb {T}), and for \lambda _n=(|n|+1)^{-1}, a Hardy type inequality for Jacobi expansions is immediate which has ever been proved by Kanjin and Sato [Math. Inequal. Appl. 7 (2004), pp. 551–555]. [ABSTRACT FROM AUTHOR]

In this paper we discuss various refinements and generalizations of a theorem of Sankar Dutta and Paul Roberts. Their theorem gives a criterion for $ d$-dimensional Noetherian Cohen-Macaulay local ring to be a system of parameters, i.e., to have height $ d$ [ABSTRACT FROM AUTHOR]

We study the almost Daugavet property, a generalization of the Daugavet property. We analyze what kind of subspaces and sums of Banach spaces with the almost Daugavet property have this property as well. The main result of the paper is that if $ Z$ such that the quotient space $ X/Z$, then $ Z$ [ABSTRACT FROM AUTHOR]