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Let L denote your first list:
sage: L = [['1.1 1.2 1.3'], ['2.1 2.2 2.3'], ['3.1 3.2 3.3'], ['4.1 4.2 4.3']]
You can see that is is a list of lists where each second-level list has a single element that is a string.
sage: L[0][0]
'1.1 1.2 1.3'
sage: L[1][0]
'2.1 2.2 2.3'
sage: L[2][0]
'3.1 3.2 3.3'
Let us pick one as an example:
sage: s = L[0][0]
sage: s
'1.1 1.2 1.3'
This string is a concatenation of strings separated with space. We can split this long string into a list of shorter strings with respect to the space separator:
sage: s.split(' ')
['1.1', '1.2', '1.3']
We get a list of strings, each representing a floating-point number. Let us transform such stings into genuine floating-point numbers:
sage: [RDF(i) for i in s.split(' ')]
[1.1, 1.2, 1.3]
Putting everything together (i.e. iterating over all the elements of the list L that are lists with a single string in them), we get:
sage: [[RDF(i) for i in M[0].split(' ')] for M in L]
[[1.1, 1.2, 1.3], [2.1, 2.2, 2.3], [3.1, 3.2, 3.3], [4.1, 4.2, 4.3]]
