diff --git a/src/spaces/homspace.jl b/src/spaces/homspace.jl
index 6e5153e83..8460f7578 100644
--- a/src/spaces/homspace.jl
+++ b/src/spaces/homspace.jl
@@ -91,7 +91,8 @@ sector structure of `W` (ignoring degeneracy dimensions).
 
 See also [`hasblock`](@ref), [`blockstructure`](@ref).
 """
-blocksectors(W::HomSpace) = sectorstructure(W).blocksectors
+blocksectors(W::HomSpace) =
+    sectortype(W) === Trivial ? _blocksectors(W) : sectorstructure(W).blocksectors
 
 function _blocksectors(W::HomSpace)
     sectortype(W) === Trivial &&
@@ -130,7 +131,7 @@ hasblock(W::HomSpace, c::Sector) = c in blocksectors(W)
 Return the total dimension of a `HomSpace`, i.e. the number of linearly independent
 morphisms that can be constructed within this space.
 """
-dim(W::HomSpace) = degeneracystructure(W).totaldim
+dim(W::HomSpace) = sectortype(W) === Trivial ? prod(dims(W)) : degeneracystructure(W).totaldim
 
 dims(W::HomSpace) = (dims(codomain(W))..., dims(domain(W))...)
 
diff --git a/src/tensors/indexmanipulations.jl b/src/tensors/indexmanipulations.jl
index 17c23e026..7155bb4be 100644
--- a/src/tensors/indexmanipulations.jl
+++ b/src/tensors/indexmanipulations.jl
@@ -254,8 +254,7 @@ function permute(
 
     # general case
     tdst = similar(t, promote_permute(t), permute(space(t), p))
-    levels = ntuple(identity, numind(t))
-    return @inbounds braid!(tdst, t, p, levels, One(), Zero(), backend, allocator)
+    return @inbounds permute!(tdst, t, p, One(), Zero(), backend, allocator)
 end
 function permute(t::AdjointTensorMap, (p₁, p₂)::Index2Tuple; kwargs...)
     p₁′ = adjointtensorindices(t, p₂)
@@ -306,6 +305,10 @@ See also [`braid`](@ref) for creating a new tensor.
         backend::AbstractBackend = TO.DefaultBackend(), allocator = TO.DefaultAllocator()
     )
     @boundscheck spacecheck_transform(braid, tdst, tsrc, p, levels)
+    if has_array_view(tdst) && has_array_view(tsrc)
+        TO.tensoradd!(tdst[], tsrc[], p, false, α, β, backend, allocator)
+        return tdst
+    end
     levels1 = TupleTools.getindices(levels, codomainind(tsrc))
     levels2 = TupleTools.getindices(levels, domainind(tsrc))
     transformer = treebraider(tdst, tsrc, p, (levels1, levels2))
@@ -377,6 +380,10 @@ end
         backend::AbstractBackend = TO.DefaultBackend(), allocator = TO.DefaultAllocator()
     )
     @boundscheck spacecheck_transform(transpose, tdst, tsrc, p)
+    if has_array_view(tdst) && has_array_view(tsrc)
+        TO.tensoradd!(tdst[], tsrc[], p, false, α, β, backend, allocator)
+        return tdst
+    end
     transformer = treetransposer(tdst, tsrc, p)
     return @inbounds add_transform!(tdst, tsrc, p, transformer, α, β, backend, allocator)
 end
diff --git a/src/tensors/tensoroperations.jl b/src/tensors/tensoroperations.jl
index 52f4eb417..147d27b16 100644
--- a/src/tensors/tensoroperations.jl
+++ b/src/tensors/tensoroperations.jl
@@ -47,6 +47,10 @@ function TO.tensoradd!(
         α::Number, β::Number,
         backend, allocator
     )
+    if has_array_view(C) && has_array_view(A)
+        TO.tensoradd!(C[], A[], pA, conjA, α, β, backend, allocator)
+        return C
+    end
     if conjA
         A′ = adjoint(A)
         pA′ = adjointtensorindices(A, _canonicalize(pA, C))
@@ -320,31 +324,22 @@ function contract!(
     )
     length(pA[2]) == length(pB[1]) ||
         throw(IndexError("number of contracted indices does not match"))
-    N₁, N₂ = length(pA[1]), length(pB[2])
 
     # find optimal contraction scheme by checking the following options:
     # - sorting the contracted inds of A or B to avoid permutations
     # - contracting B with A instead to avoid permutations
+    pA′, pB′, pA″, pB″, pAB′ = _contract_candidates(pA, pB, pAB)
 
-    qA = TupleTools.sortperm(pA[2])
-    pA′ = Base.setindex(pA, TupleTools.getindices(pA[2], qA), 2)
-    pB′ = Base.setindex(pB, TupleTools.getindices(pB[1], qA), 1)
-
-    qB = TupleTools.sortperm(pB[1])
-    pA″ = Base.setindex(pA, TupleTools.getindices(pA[2], qB), 2)
-    pB″ = Base.setindex(pB, TupleTools.getindices(pB[1], qB), 1)
+    # dims are permutation-invariant, so compute them once here rather than in every memcost call
+    dA, dB, dC = dim(A), dim(B), dim(C)
 
     # keep order A en B, check possibilities for cind
-    memcost1 = TO.contract_memcost(C, A, pA′, B, pB′, pAB)
-    memcost2 = TO.contract_memcost(C, A, pA″, B, pB″, pAB)
+    memcost1 = _contract_memcost(dA, dB, dC, C, A, pA′, B, pB′, pAB)
+    memcost2 = _contract_memcost(dA, dB, dC, C, A, pA″, B, pB″, pAB)
 
     # reverse order A en B, check possibilities for cind
-    pAB′ = (
-        map(n -> ifelse(n > N₁, n - N₁, n + N₂), pAB[1]),
-        map(n -> ifelse(n > N₁, n - N₁, n + N₂), pAB[2]),
-    )
-    memcost3 = TO.contract_memcost(C, B, reverse(pB′), A, reverse(pA′), pAB′)
-    memcost4 = TO.contract_memcost(C, B, reverse(pB″), A, reverse(pA″), pAB′)
+    memcost3 = _contract_memcost(dB, dA, dC, C, B, reverse(pB′), A, reverse(pA′), pAB′)
+    memcost4 = _contract_memcost(dB, dA, dC, C, B, reverse(pB″), A, reverse(pA″), pAB′)
 
     return if min(memcost1, memcost2) <= min(memcost3, memcost4)
         if memcost1 <= memcost2
@@ -361,23 +356,37 @@ function contract!(
     end
 end
 
-function TO.contract_memcost(
-        C::AbstractTensorMap,
-        A::AbstractTensorMap, pA::Index2Tuple,
-        B::AbstractTensorMap, pB::Index2Tuple,
-        pAB::Index2Tuple
+# @noinline to avoid specialization
+@noinline function _contract_candidates(pA::Index2Tuple, pB::Index2Tuple, pAB::Index2Tuple)
+    N₁, N₂ = length(pA[1]), length(pB[2])
+
+    qA = TupleTools.sortperm(pA[2])
+    pA′ = Base.setindex(pA, TupleTools.getindices(pA[2], qA), 2)
+    pB′ = Base.setindex(pB, TupleTools.getindices(pB[1], qA), 1)
+
+    qB = TupleTools.sortperm(pB[1])
+    pA″ = Base.setindex(pA, TupleTools.getindices(pA[2], qB), 2)
+    pB″ = Base.setindex(pB, TupleTools.getindices(pB[1], qB), 1)
+
+    pAB′ = (
+        map(n -> ifelse(n > N₁, n - N₁, n + N₂), pAB[1]),
+        map(n -> ifelse(n > N₁, n - N₁, n + N₂), pAB[2]),
     )
+    return pA′, pB′, pA″, pB″, pAB′
+end
+
+function _contract_memcost(dimA, dimB, dimC, C, A, pA, B, pB, pAB)
     ipAB = TO.oindABinC(pAB, pA, pB)
-    return dim(A) * (!TO.isblascontractable(A, pA) || eltype(A) !== eltype(C)) +
-        dim(B) * (!TO.isblascontractable(B, pB) || eltype(B) !== eltype(C)) +
-        dim(C) * !TO.isblasdestination(C, ipAB)
+    return dimA * (!TO.isblascontractable(A, pA) || scalartype(A) !== scalartype(C)) +
+        dimB * (!TO.isblascontractable(B, pB) || scalartype(B) !== scalartype(C)) +
+        dimC * !TO.isblasdestination(C, ipAB)
 end
 
 function TO.isblascontractable(A::AbstractTensorMap, pA::Index2Tuple)
-    return eltype(A) <: LinearAlgebra.BlasFloat && has_shared_permute(A, pA)
+    return scalartype(A) <: LinearAlgebra.BlasFloat && has_shared_permute(A, pA)
 end
 function TO.isblasdestination(A::AbstractTensorMap, ipAB::Index2Tuple)
-    return eltype(A) <: LinearAlgebra.BlasFloat && has_shared_permute(A, ipAB)
+    return scalartype(A) <: LinearAlgebra.BlasFloat && has_shared_permute(A, ipAB)
 end
 
 function blas_contract!(