Bringing together research that was otherwise scattered throughout the literature, this book
collects the main results on the conditions for the existence of large algebraic substructures …

For the last decade there has been a generalized trend in mathematics on the search for
large algebraic structures (linear spaces, closed subspaces, or infinitely generated …

Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is
called lineable whenever A contains, except for zero, an infinite dimensional vector …

In this article, we investigate the existence of closed vector subspaces (ie spaceability) in
various nonlinear subsets of Orlicz-Lorentz spaces $\Lambda_ {\varphi, w} $, equipped with …

Under natural assumptions about the measure spaces, the topological size as well as the
algebraic size of the family of measurable real functions on the product measure space …

Suppose A is a subset of a Banach lattice (Banach algebra) X. We look for “large” sublattices
(resp. subalgebras) of A. If X is a Banach lattice, we prove:(1) If Y is a closed subspace of X …

The algebraic properties of sets of functions have been investigated in the Real Analysis for
many years. The direction example of such a research is the idea of finding maximal additive …

In this paper, we study the existence of infinite dimensional closed linear subspaces of a
rearrangement invariant space on [0, 1] every nonzero element of which does not belong to …

In 1951 V. Jarník constructed two continuous functions whose Volterra convolution is
nowhere differentiable. We generalize Jarníkʼs results by proving that the set of such …

In this paper, we consider the size of the set\big {(f, g) ∈ ℓ^ p (S) * ℓ^ q (S): ∃\, x ∈ S,\,| f|*|
g|(x)< ∞\big\}(f, g)∈ ℓ p (S)× ℓ q (S):∃ x∈ S,| f|∗| g|(x)<∞, where p ∈ (1,+ ∞) p∈(1,+∞), q …